blackpenredpen
Do We REALLY Have More Integers?
updated
The solution to the derivative challenge problem: youtu.be/V9rrLp2CpPw?si=SadRcaYGZUVruIuj
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The afterward youtu.be/9GFUyT-D6D0
Try the paper first: qualifications.pearson.com/content/dam/pdf/A-Level/Mathematics/2017/Exam-materials/9fm0-01-que-20220526.pdf
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Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Erik S. Mark M, Phillippe S., Nicole D.
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๐ช Support this channel and get my math notes by becoming a patron: patreon.com/blackpenredpen
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Timestamps:
0:00 A-Level further math paper from June 2022
0:58 Q1 Solving a cubic equation with complex roots
6:23 Q2 Solving a 4-th degree hyperbolic equation
15:55 Q3 Solving a first-order linear differential equation with integrating factor
21:28 Q4 Solving a series problem with natural log
28:55 Q5 Finding the determinant and the inverse of a 3x3 matrix
40:50 Q6 Partial fraction decomposition & integral of a rational function
50:05 Q7 A complex number problem
1:00:11 Q8 A long trig identity
1:23:39 Q9 An improper integral with hyperbolic cosine
Here's the last question from the 2022 GCSE maths paper that made the news. We have three circles as shown and each radius is 4 cm. We have to find the area of the shaded region in the middle. I made a horrible mistake last time when I said the area of a circular sector is r*theta. The correct formula should be A=1/2*r^2*theta and theta has to be in radians.
My first time doing a British GCSE maths paper: youtu.be/rJXfUiSwBzU?si=Ps79fuXWQ1xiQ_In
Reddit: reddit.com/r/theydidthemath/comments/12oholz/self_last_years_gcse_maths_question_that_made_the
The Sun News: thesun.co.uk/news/18647879/kids-left-baffled-impossible-gcse-question
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Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Erik S. Mark M, Phillippe S.
๐ช Get my math notes by becoming a patron: patreon.com/blackpenredpen
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
We will go over ALL the free response questions from the 2023 AP Calculus AB test to help you prepare for the upcoming AP exam. Topics included defined integral, average value of a function on an interval, change in position vs total distance traveled, implicit differentiation, related rates, derivative from a table, and more. Try all the questions first: apcentral.collegeboard.org/media/pdf/ap23-frq-calculus-ab.pdf and best of luck on your AP calculus test!
2 series problems from the AP Calc BC FRQ: youtu.be/pHSFB8_W3mc
Try this AP calculus BC FRQ from 2004: youtu.be/DHDC3oOy178?si=SpIiIByrPIJ6s615
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Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Erik S. Mark M, Phillippe S.
๐ช Get my math notes by becoming a patron: patreon.com/blackpenredpen
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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#blackpenredpen #math #calculus #apcalculus
0:00 AP calculus exam is coming!
0:15 Thanks to Brilliant for sponsoring this video
1:13 Q1
15:41 Q2
27:39 Q3 differential equation
43:29 Q4
1:04:30 Q5
1:15:30 Q6
This system of nonlinear equations is from the general round of the 2023 Harvard-MIT math tournament. hmmt.org/www/archive/271 I will present the linear algebra method I learned from their official solution to solve this system because I thought it was fascinating. It's from Harvard and MIT, of course, it is awesome!
3 ways of finding the determinant of a 3x3 matrix: youtube.com/watch?v=TkNeDxoRikY
Try "my first Harvard-MIT math tournament problem": youtu.be/jQuArBZO7PI?si=EvMgqNNDPHFZMppU
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(A) 0 to the 0th power=1 or undefined. No calculus limit here.
(B) sqrt(1) = 1 or both +-1?)
(C) 0.999...=1 or not?
(D) order of operations 12/3(4)=1 or 16
More than 28,000 viewers voted in my recent poll and now let's discuss what each debate is all about.
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#blackpenredpen #math
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#blackpenredpen #math #calculus #equation
Subscribe to @blackpenredpen for more fun math videos.
We will solve this power equation x^ln(4)+x^ln(10)=x^ln(25). However, the process of solving this equation would require making one side equal to 0 but factoring every term by x^ln(4), and I don't think the expressions will look that nice. So instead, we can use the log property that a^logb(c)=c^logb(a) and change the equation to an exponential equation. The answer will involve the usage of the quadratic formula and we will also see the golden ratio.
Equation-of-the-year playlist: youtube.com/playlist?list=PLj7p5OoL6vGxHsQjgCw5Nfe8O3o8fu3LV
0:00 Math for fun, solving the power equation x^ln(4)+x^ln(10)=x^ln(25)
1:09 Proving a^logb(c)=c^logb(a)
3:18 Solving the equation in exponential form
8:35 Check out Brilliant
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#blackpenredpen #math #calculus #apcalculus
This is my first video on a multi-variable limit that you will see in your Calculus 3 class. We will evaluate the limit of y/x as (x,y) goes to (0,0) but how do we take care of this? We do get 0/0 indeterminate form but can we use L'Hopital's rule?
0:00 Limit of y/x as (x,y) goes to (0,0)
9:47 Check out today's sponsored, Brilliant!
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We will solve the equation that has two square roots sqrt(16-x^2)+sqrt(9-x^2)=5 with a cool geometric triangle trick. In the end, we will also see if ChatGPT can solve this equation by using geometry. Check out a similar video on the proof of the Pythagorean Theorem and its inverse: youtu.be/itfXCKpmQPs
0:00 Solving sqrt(16-x^2)+sqrt(9-x^2)=5 by using geometry
5:15 Check out Brilliant
6:13 Can ChatGPT solve this with geometry?
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan Abdennor Bel Tobias V Killbot2525 Stephen Ripple Spam Email YKTV # bruh Amanda Skelton
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Thank you all!
Today we will find a general solution to the transcendental equation a^x+bx+c=0. Here's an example 2^x-3x-1=0 youtu.be/GJbzsmccFtw
Check out a detailed the Lambert W function introduction: youtu.be/Qb7JITsbyKs?si=bKnZW_lqlDjiKQuf
0:00 solve a^x+bx+c=0
7:02 Check out Brilliant
8:06 bonus part (the conditions on this formula)
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan Abdennor Bel Tobias V Killbot2525 Stephen Ripple Spam Email YKTV # bruh Amanda Skelton
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Thank you all!
๐ Shop Ultimate calc 2 integral sweatshirt: amazon.com/dp/B0C9L798F2
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
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Thank you all!
Check out my 100 calculus 2 problems to help you with your calc 2 final: youtu.be/Kwyk_mteyNc?si=Dj_3rv2qeen7SiMi
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#blackpenredpen #math #calculus #apcalculus
Related videos:
youtu.be/VAScsSpfKv8?si=UIO7P0ccOAUnxQCs
youtube.com/watch?v=57Eawy5IAaM
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
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Thank you all!
The usual exponent rules are pretty easy to see when the exponents are whole numbers. For example, we know e^2 means e*e and e^3 means e*e*e, so e^2*e^3=e*e*e*e*e*e=e^5. But what if we have rational exponents such as e^(1/2)*e^(1/3)? How do we prove the rule of exponent in this case is equal to e^(5/6)?
Proving e^x*e^y=e^(x+y) by power series: youtu.be/r87AfxUwD60
Deriving the power series of e^x centered at 0: youtu.be/1OhMpXFb6yI?si=2u-5z1KINQPLz6sK
Check out the binomial theorem: youtu.be/cvhyJT9c0ac?si=2brCzT8yH5uAslkd
The Power Series For You merch
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0:00 We know e^2*e^3=e^(2+3), but what if we have e^(1/2)*e^(1/3)?
1:12 Proving e^(1/2)*e^(1/3) by using power series
3:14 Cauchy product of two infinite series
7:38 Back to the proof
14:42 Check out Brilliant
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
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Thank you all!
0:00 finding the second derivative of sin(x^2) but no differentiation shortcuts
0:54 Definition of derivative, symmetric derivative, and second symmetric derivative in terms of limits
7:46 The real action!!
9:08 The formula for sin(A)+sin(B)
12:01 Back to the limit
29:50 Check the answer!
Check out my 100-limit video for more calculus limit practice. youtu.be/TglD4Y6lmQk?si=lR_jfa-gI8FVO7VS
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๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
๐ช Get my math notes by becoming a patron: patreon.com/blackpenredpen
#blackpenredpen #math #calculus #apcalculus
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
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Thank you all!
I made this all-in-one style calculus problem for you as an early Christmas gift. We will find the derivative of sin^2(x^2), which requires the chain rule twice, then we need to find a closed form for the infinite power series 1+x^2+x^4/2+x^6/6+..., then we have the limit of sqrt(x)/ln(x) and the limit of ln(x)/sqrt(x) as x goes to infinity. Finally, we will put everyone together and integrate it!
#calculus #math #challenge #blackpenredpen
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0:00 Christmas is coming, so I made an all-in-one calc 2 problem or you
0:20 limit of ln(x)/sqrt(x) as x goes to infinity
1:45 derivative of sin^2(x^2), chain rule twice!
2:57 Power series for 1+x^2+x^4/2+x^6/6+...
4:00 solving the integral
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
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Thank you all!
Subscribe to @blackpenredpen for more fun math lessons.
#calculus #trigonometry #math #mathforfun #blackpenredpen
Check out the related videos:
log triangle problem: youtu.be/CMdJPwEbE8A
exp triangle problem: youtu.be/qKytYveIOmA?si=tujFerP3CccFKJrV
triple angle identity for sine: youtu.be/aSq9vwGHLTg
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
Whatโs the Lambert W function? youtu.be/Qb7JITsbyKs?si=05xAbHwlaj9ChD_W
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
#blackpenredpen #math #mathforfun
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
Here's a challenging integral for Calculus 2 students! We will evaluate the improper integral 1-e^(-1/x^2) from 0 to infinity. This integral actually converges thanks to the "1-". This integral is closely related to the most famous integral in the world, the Gaussian integral. In fact, we can use integration by parts, u-substitution, and L'Hosptial's rule to make the connection with the Gaussian integral. This can be given to any calculus 2 or calculus 3 students if they would like to have a challenging integral. #calculus #mathforfun #blackpenredpen
Check out the related videos:
How Laplace solved the Gaussian integral, ๐ youtu.be/tCPQSobqFh4?si=eCeLOIRLl9CrL7Lv
The original way with polar coordinate ๐ youtu.be/7kvxMrbPvhs?si=YCjkwB1g5iMPa7o1
The error function introduction ๐ youtu.be/jkytxdedxhU?si=cJJfu1ibrgrLjIlV
0:00 My pick for the most famous integral in the world
0:14 integral of 1-e^(-1/x^2) from 0 to inf
9:17 Check out Brilliant
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
Subscribe to @blackpenredpen so you don't miss the "fixed point iteration" video!
Lambert W function introduction: youtu.be/Qb7JITsbyKs?si=5z1DnLDsqUgGsocc
For another challenge, check out this video: youtu.be/Rg3dBosfZ3Y?si=Zmdy1Y_YnJJOFCPW
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
#algebra #math #blackpenredpen
Check out 0^0 approaches e: youtu.be/zyQtN7Zbi-c
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
#calculus #math #mathforfun #blackpenredpen
how calculus teachers create integrals for your test! I took me about an hour to craft this integral which features all the trigonometric functions, the natural logarithm function, the pi-th power, and a derivative for the denominator. This integral looks scary but the solution is actually very straightforward! Enjoy! #calculus #math #trigonometry #blackpenredpen
Check out my 100 integrals for more integration practice for your Calculus 1 or Calculus 2 class. youtu.be/dgm4-3-Iv3s?si=lTybJlpTMFdQINXr
0:00 how calculus teachers create integrals for your test
6:30 check out Brilliant:
7:25 BOOM!
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
If you would also like to sponsor BMT, please visit: https://berkeley.mt/sponsors/
This calculus tutorial contains the solution to the 2022 Berkeley Math Tournament calculus tiebreaker! It contains a limit, derivative, and an integral at calculus 2 (i.e. AP calculus BC) level. The time limit is 15 minutes but you will also have to race with other times during the tournament. I love these math competition problems because they really force you to think and they really challenge your problem-solving skills. It's okay if you can't solve these competition problems. I, too, can't solve many of them either. It really takes lots of effort and practice in order to be good at these. Finally, I just want to tell you, to be sure to enjoy the learning process and have fun!
0:00 2022 Berkeley Math Tournament calculus tiebreaker
0:08 Q1, evaluate a limit with an integral
3:10 Q2, find the 2022nd derivative of f(x)=e^x*sin(x) at x=0
7:36 Q3, evaluate the integral of arctan(x)/x from 1/e to e
#calculus #tutorial #berkeley #blackpenredpen
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
Check out how to differentiate the quadratic formula: youtu.be/JEcE-wDRMCk?si=Uq1p1KYNj-Kpu5g2
0:00 We will integrate the quadratic formula
7:48 ChatGPT vs integral of the quadratic formula
๐ Shop the Gaussian Integral t-shirt: amzn.to/45jTJnt
๐ช Get my math notes by becoming a patron: patreon.com/blackpenredpen
#blackpenredpen #math #calculus #apcalculus #tutorial
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov Roy Logan
----------------------------------------
Thank you all!
๐ Euler's Identity e^(iฯ)+1=0 t-shirt: amzn.to/427Seae
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke Jorge Casanova Alexis Villalobos Jm Law Siang Qi Tancredi Casoli Steven Sea Shanties Nick K Daniel Akheterov
----------------------------------------
Thank you all!
Today we will see what your first 5 days in your calculus 2 or AP calculus BC class is like. Calculus 2 is known as integral calculus and we usually start with learning all the integration techniques. We will cover the integral of x^2 with the reverse power rule, the integral of x*e^(x^2) with u-substitution, the integral of x^2*e^x with integration by parts, the integration of sqrt(1+x^2) with trigonometric substitution, and the integration of (2x+1)/(x^2+3x+2) with partial fraction decomposition.
0:00 day 1, reverse power rule
0:20 day 2, u sub
1:27 day 3, integration by parts
2:29 day 4, trig sub
6:16 day 5, partial fraction decomposition
8:51 Check out Brilliant
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
----------------------------------------
Thank you all!
#blackpenredpen #math #calculus #tutorial
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
----------------------------------------
Thank you all!
#trigonometry #math #precalculus
File ๐ patreon.com/posts/24-trig-identity-88803595
Solutions ๐ patreon.com/posts/my-hand-written-88804184
๐ Shop my math t-shirt & hoodies: amzn.to/3qBeuw6
Thanks to @takureido3122 & @sohampinemath1086 for the time stamps!!!
Intro - 00:00
1 - 00:51 โ sinx+cotxcosx
2 - 04:40 โ (secx-cosx)/sinx
3 - 07:16 โ cotx/(cscx-sinx)
4 - 09:00 โ (1+2cosx)/(2+secx)
5 - 10:45 โ 1/(1-sinx)+1/(1+sinx)
6 - 13:00 โ (2+cotยฒx)/cscยฒx-1
7 - 15:36 โ tan(x+ฯ/4)
8 - 19:11 โ cos(3x)
9 - 24:09 โ cos(4x)
10 - 29:32 โ sec(sin^-1x)
11 - 32:42 โ cos(2tan^-1x)
12 - 36:56 โ tan(2sin^-1x)
13 - 42:44 โ cscยฒx+secยฒx
14 - 45:41 โ cosx cos(2x)
15 - 49:38 โ sinโดx
16 - 57:22 โ sinโดx-cosโดx
17 - 1:02:04 โ tanx+tany
18 - 1:04:47 โ 2tanx/(1+tanยฒx)
19 - 1:07:25 โ 1/(secx-1)+1/(secx+1)
20 - 1:12:08 โ (sinx+tanx)/(1+cos(-x))
21 - 1:16:14 โ cosยฒx-sinโดx secยฒx
22 - 1:14:50 โ (sinx+cosx)ยฒ
23 - 1:20:18 โ sinx/(1-cotx)+cosx/(1+tanx)
24 - 1:23:57 โ secยฒ(x/2)
----------------------------------------
๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
----------------------------------------
Thank you all!
File (public): ๐ patreon.com/posts/24-rigorous-88483708
My hand-written notes for all these 24 proofs: (Patreons only) ๐patreon.com/posts/notes-for-24-88670205
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0:00 24 limit proofs with definitions
Q1. 0:29 epsilon-delta proof, linear case
Q2. 3:51 epsilon-delta proof, rational function
Q3. 12:04 epsilon-N proof, x approaching infinity, rational function
Q4. 17:18 M-delta proof, x approaching infinity, rational function
Q5 22:19 epsilon-N proof
Q6 28:34 epsilon-delta proof, quadratic case
Q7 32:26 M-N proof, square root function
Q8 36:06 epsilon-delta proof, square root function
Q9 42:47 ฮตฮด linear case
Q10 45:00 ฮตฮด limit proof, *hard*
Q11 52:21 limit of 1/x^2 as x goes to infinity
Q12 55:17 limit of sqrt(x-3) as x goes to infinity
Q13 58:24 limit of x^3 as x goes to 2
Q14 1:04:43 ฮตฮด linear case
Q15 1:06:40 ฮตN proof
Q16 1:15:50
Q17 1:19:00
Q18 1:21:50
Q19: 1:26:46
Q20: 1:30:07
*start at 1:31:41, please change all the ฮต to M
Q21 1:32:24
Q22 1:36:42
Q23 1:41:21
*at 1:42:28, it should be 1/abs(x-3) is greater than 1/ฮด. And then say 1/(abs(x-3))^2=1/(x-3)^2 is greater than 1/ฮด^2
Q24 1:44:15 limit of x^2/(x+1) as x goes to infinity
*at 1:48:26, we need to add the condition that N is greater than 1. So please write N=max{1, 2ฮต}
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Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
----------------------------------------
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#calculus #GPAsaver #math #blackpenredpen
#calculus #math #blackpenredpen
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
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Thank you all!
The integral of x*sin(x)/(1+cos^2(x)) from 0 to pi is actually a famous exam problem integral. I saw a post on Dcard about this integral and I just had to integrate it. I use the property that the integral of f(x) from a to b is the same as the integral of f(a+b-x) from a to b. This is commonly known as the king property and I have a proof here: youtu.be/9xaGYqiOkPM?si=eXQuXRoHdvUbI2CQ
#calculus #math #maths #exam
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Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
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#calculus #math #maths #college #blackpenredpen
This is similar to the epsilon-delta proofs for limits and you can check out that introduction here: ๐ youtu.be/DdtEQk_DHQs
0:00 I will help you understand the ฮตN definition for a finite limit at infinity
0:19 the 4 main cases of a rigorous definition of a limit
2:24 the ฮตN definition
4:14 how to easily write a rigorous limit proof
11:32 an actual example with ฮต=0.02 and find a N
#calculus #blackpenredpen #realanalysis #math #college
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
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Thank you all!
Regular math: Compute the sum of all positive divisors of the number 186
Competition math: Compute the sum of all positive integers whose positive divisors sum to 186.
This competition problem is from the 2022 Princeton University Math Competition, the number theory section. As you will see, the competition problem requires way more math knowledge and thinking rather than just a standard routine process. This is also a reason why it is more fun to solve math competition problems.
Princeton University Math Competition site: jason-shi-f9dm.squarespace.com
The test: static1.squarespace.com/static/570450471d07c094a39efaed/t/642cf9f637301b7f0aa1d2e3/1680669174825/Number_Theory_B_2022_.pdf
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Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
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Thank you all!
I saw this beautiful question from the 2020 Oxford Math Admissions Test, which was for both math and computer science applicants. The question has multiple parts but the first part gives away a very big hint, so I decided to modify this question a bit and present it to you guys. I am sure this could easily be a math competition-level problem and I had tons of fun solving it! See the original Oxford math and computer science admissions test problem on page 8 here:
maths.ox.ac.uk/system/files/attachments/test20_0.pdf
0:00 I modified an Oxford math admission problem
24:07 Check out Brilliant
#math #blackpenredpen #oxford #numbertheory
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Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
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Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
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Thank you all!
This question is from the Stanford Math Tournament (SMT) the algebra tiebreaker section stanfordmathtournament.com/archive/2023. We are given a cubic function f(x)=x^3-6x^2+25/2x-7 and we know there exists a closed interval [a,b] such that the sequence x, f(x), f(f(x)), ... is bounded for x on [a, b]. This question is fascinating because not all cubic functions have such properties. I will use the fixed-point approach for this problem, how would you solve this? #brilliant #math #stanford #blackpenredpen
0:00 Stanford Math Tournament algebra tiebreaker
1:00 Check out Brilliant
2:10 My solution to this problem
7:12 Why my solution works for this problem
Note: I avoided calculus derivative here because I wanted to keep it with just algebra. I will do another video on the fixed-point iteration later.
9:56 the official solution
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Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric Maximilian Mecke
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Thank you all!
#algebra #math #blackpenredpen
worksheet ๐ patreon.com/posts/my-algebra-only-81417933
my written solution ๐ patreon.com/posts/my-algebra-81418158
0:00 24 quadratic equations with only "1, 2, 3, 4"
0:31 Q1, solving a quadratic equation by factoring
4:55 Q2, by taking the square roots on both sides
9:43 Q3, expand first, then solve by factoring
14:00 Q4, completing the square
20:14 Q5, the quadratic formula
26:40 Q6
30:03 Q7
33:52 Q8
36:11 Q9
37:55 Q10
43:10 Q11
45:28 Q12
48:10 Q13
50:37 Q14
52:07 Q15, a special way to complete the square
59:00 Q16
1:00:30 Q17
1:02:55 Q18
1:06:03 Q19
1:12:49 Q20,
1:17:02 Q21, quadratic equation with complex solutions
1:20:12 Q22,
1:23:49 Q23,
1:32 44 Q24,
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric
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Thank you all!
Can the power of the imaginary unit i ever give us 2? We know i^1=1, i^2=-1, i^3=-i, i^4=1, and so on. So is it possible for us to find x so that i^x=2? Well, the answer is yes but it is not real. #ComplexNumbers #Exponentiation #ImaginaryNumbers #Mathematics #blackpenredpen
0:00 We know i^1=1, i^2=-1, i^3=-i, i^4=1, and so on. So is it possible for us to have i^x=2?
7:35 Check out Brilliant
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
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Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric
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Thank you all!
Notes on Patreon: patreon.com/posts/notes-on-sin-x-3-82966449
Cubic formula: youtu.be/ULsPhWmqhyc
Check out my unit circle tee on Amazon: amzn.to/3O9jge7
Why sin(50 degrees) and sin(70 degrees) showed up: youtu.be/JqagcCrdpQQ
0:00 what's a formula for sin(x/3), i.e. 1/3 angle formula for sine
0:23 deriving sin(3x) by using double-angle formula
4:34 using the cubic formula (the depressed version)
11:11 attempting to get sin(10 degrees) but we ran into some issues
19:11 finally got sin(10 degrees)
but I wonder if we can write sin(10 deg) as a radical expression without using the imaginary unit i
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Andr3w11235 Cadentato Joe Wisniewski Eric
----------------------------------------
Thank you all!
Notes for this video are available on my Patreon: ๐ patreon.com/posts/notes-proof-of-82385985
Introduction and more examples of the epsilon-delate definition of a limit: ๐youtube.com/playlist?list=PLj7p5OoL6vGwzCW5N_hyGa88BzGQHv1ax
0:00 Review some limits and their epsilon-delta definition
2:48 The proof!
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall Eric
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Thank you all!
I came up with this tricky test question challenge for my precalculus students. Start with an obtuse triangle, give students the length of all three sides and one of the acute angles. Ask the students to find the measure of the obtuse angle. Now many students will proceed by using the Law of Sine because the formula is shorter compared to the Law of Cosine. But because the range of the inverse sine function is _________, we will have to be extra careful with we use the Law of Sine!
Written solutions for this problem: patreon.com/posts/81996867
My trig worksheets (for anyone): patreon.com/posts/81996734
Here's another precalculus challenge: youtu.be/-aedH9Pusr4
Proofs of the Law of Sine & Cosine: youtu.be/843Uw-Hj-OQ
#precalculus #math #blackpenredpen #mathteacher
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt Zahra Parhoun Hassan Alashoor Kaakaopuupod bbaa Joash Hall
----------------------------------------
Thank you all!
0:00 my favorite precalculus test question
5:02 a small mistake. c should be 5.8
8:24 Check out Brilliant
de Moivre quintic formula ๐ youtu.be/L8W684pCHyc
0:00 we will derive the cubic formula
0:07 review on solving the quadratic equation x^2+px+q=0 and the pq-formula
6:17 part1, get rid of the x^2 term in the y-world (let x=y-b/(3a))
17:23 part 2, solving y^3+py+q=0 (let y=z-p/(3z))
39:27 part 3, put everything together
#maths #imaginarynumber #blackpenredpen
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AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt bbaa Joash Hall
----------------------------------------
Thank you all!
We will tackle a famous calculus problem using the definition of the derivative, forcing even the most confident students to dig deep and truly understand the concept. Watch as we derive the derivative of f(x)=x^2*sin(1/x), including the challenging part of handling the derivative at x=0, where the function is not differentiable. But we don't stop there - we also introduce the squeeze theorem, a powerful tool to evaluate limits, to further deepen our understanding of calculus. This video is perfect for anyone looking to enhance their calculus knowledge and master the fundamental concepts of derivatives.
Related video: Calculus Teacher vs Power Rule Students: youtu.be/57Eawy5IAaM
0:00 If you are also a calculus teacher
0:39 f(x)=x^2*sin(1/x) when x is not 0 and f(0)=0
7:13 check out Brilliant
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10% off with the code "WELCOME10"
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๐ช Support the channel and get featured in the video description by becoming a patron: patreon.com/blackpenredpen
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt
----------------------------------------
Thank you all!
Read more on involutory functions: en.wikipedia.org/wiki/Involution_(mathematics)
0:00 how I have fun when I teach math classes
0:33 the precalculus way to find the inverse of a function
3:28 finding the involution for rational functions
13:21 a much better way!
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***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do***
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt
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In this video, we will show you why your calculus students deserve to learn and use the DI method for integration by parts. While it's true that the DI and u-dv methods are equivalent, the DI method has many advantages. It's simpler, more intuitive, and it reduces the risk of mistakes. By using the DI method, your students will be able to tackle more complex integration problems with ease. We'll go over examples of integrating x^2ln(x) and x^2cos(x) using both methods, and you'll see for yourself how much easier and faster the DI method is. Don't let your students struggle with the traditional u-dv method any longer! #calculus #integrationbyparts #DIMethod #blackpenredpen #matheducation
Here are the 3 stops for the DI method: youtube.com/watch?v=2I-_SV8cwsw
Why I don't teach the LIATE method: youtu.be/z33rYYUM4d8
0:00 integral shortcut? answer in 5 seconds : )
0:07 why i am making this video
0:43 proving the integration by parts formula
2:02 example 1, integral of x^2*ln(x)
5:30 why the DI method is really the same as integration by parts
8:34 example 2, the integral that got 6M+ views on Instagram
12:22 using DI method for the integral of x^2*cos(x)
15:56 check out Brilliant
Follow me on Instagram: instagram.com/blackpenredpen
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***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do***
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald Yuval Blatt
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We know the principal square root of -1 is the imaginary unit i but what if we have the i-th root of -1? We will do a quick review on converting a complex number from the standard form a+bi to its polar form re^(i*theta). Then we will see the surprising answer that the i-th root of -1 will actually give us.
Related videos:
the proof of the Euler's identity (with the Taylor series): youtu.be/Jqt67tJCiwQ
i-th root of i: youtu.be/hy-ZSvjpqlc
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0:00 what's the i-th root of -1
5:30 check out Brilliant
6:08 challenging question (-1)^pi
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***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do***
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
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Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N Anthony Rogers Mark Madsen Robert Da Costa Nathan Kean Timothy Raymond Gregory Henzie Lauren Danielle Nadia Rahman Evangline McDonald
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See the integral of sin(x)/x from 0 to infinity: youtu.be/s1zhYD4x6mY
integral of sin^2(x)/x^2 from 0 to infinity: youtu.be/jQz1gQ24OHc?t=22092
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***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do***
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N
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I solved this monster improper integral during the Extreme Calculus Calculus (another 100 integrals). Full video youtu.be/jQz1gQ24OHc
Subscribe to @bprpcalculusbasics
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***Thanks to ALL my lovely patrons for supporting my channel and believing in what I do***
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N
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Get the file & answer key on my Patreon ๐ patreon.com/posts/102752235
100 integrals (original) ๐ youtu.be/dgm4-3-Iv3s
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Big thanks to my Patrons for the full-marathon support!
Ben D, Grant S, Mark M, Phillippe S.
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Thanks to Nathaniel Barnett for the time stamps!
0:00 100 integrals part 2!
Q1, 0:00:46 integral of 2022
Q2, 0:03:03 integral by trig identities and u-sub
Q3, 0:08:23 integral by trig sub
Q4, 0:12:34 integral by u-sub and integration by parts
Q5, 0:17:02
Q6, 0:19:42
Q7, 0:30:07
Q8, 0:33:45
Q9, 0:37:58
Q10, 0:45:16
Q11, 0:48:30
Q12, 0:53:16
Q13, 0:59:06
Q14, 0:58:34
Q15, 1:00:41
Q16, 1:04:56
Q17, 1:07:27
Q18, 1:12:27
Q19, 1:14:42
Q20, 1:18:50
Q21, 1:22:30 integral of x^n*e^x
Q22, 1:25:14 integral of (ln(x))^n
Q23, 1:27:40 integral of sin^n(x)
Q24, 1:37:44 integral of tan^n(x)
Q25, 1:42:58 integral of sec^n(x)
Q26, 1:52:14
Q27, 1:54:45
Q28, 1:57:45
Q29, 2:01:49
Q30, 2:04:49
Q31, 2:24:38 integral of sec(x) by Weierstrass Substitution
Q32, 2:27:17
Q33, 2:31:25
Q34, 2:35:00
Q35, 2:37:20
Q36, 2:42:02
Q37, 2:44:24
Q38, 2:50:18
Q39, 2:51:53
Q40, 2:56:12
Q41, 3:00:21
Q42, 3:04:07
Q43, 3:06:45
Q44, 3:11:58
Q45, 3:19:02
Q46, 3:24:19
Q47, 3:28:36
Q48, 3:31:54
Q49, 3:33:44
Q50, 3:43:40
Q51, 3:49:16
Q52, 3:55:44
Q53, 3:59:50
Q54, 4:03:18 integral of x/(1+e^x)
Q55, 4:08:21 integral of e^x/(1+x)
Q56, 4:09:21 integral of e^e^x
Q57, 4:10:27 integral of ln(ln(x))
Q58, 4:12:40
Q59, 4:14:28
Q60, 4:19:48 integral of the Lambert W function
Q61, 4:25:39 improper integral of 1/x^p from 1 to inf
Q62, 4:28:52
Q63, 4:29:32
Q64, 4:32:55
Q65, 4:35:29 the Gaussian Integral
Q66, 4:50:04
Q67, 4:55:42
Q68, 4:58:36 integral of ln(x) from 0 to 1
Q69, 5:02:56
Q70, 5:10:32
Q71, 5:13:24 integral of ln(x)/(x-1) from 0 to 1
Q72, 5:21:08 integral of (x-1)/ln(x) from 0 to 1
Q73, 5:28:08 integral by symmetry
Q74, 5:34:14 integral by even and odd function properties
Q75, 5:43:16
Q76, 5:51:17
Q77, 5:52:58
Q78, 6:00:28 the Dirichlet integral, the integral of sin(x)/x from 0 to inf
Q79, 6:08:10
Q80, 6:13:28
Q81, 6:37:48 double integral & change the order of integration
Q82, 6:45:45
Q83, 6:49:24
Q84, 6:54:00
Q85, 6:57:25
Q86, 7:03:50
Q87, 7:07:33
Q88, 7:11:11
Q89, 7:17:27
Q90, 7:21:37
Q91, 7:28:52
Q92, 7:37:47
Q93, 7:55:15
Q94, 8:07:00
Q95, 8:10:24
Q96, 8:21:05
Q97, 8:22:55
Q98, 8:26: 30
Q99, 8:29: 59
Q100, 8:33:33
Q101, 8:38:32 the BIG integral from the Berkeley Math Tournament
*Thanks to ALL my lovely patrons for supporting my channel and believing in what I do*
AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano
Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley
Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel
Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev
Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist
Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen
Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata
Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff
Julian Moik Hiu Fung Lam Ronald Bryant Jan ลehรกk Robert Toltowicz
Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham
Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi
Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor. Jasmine Soni L wan na Marcelo Silva Samuel N