This problem is from a final exam for a professor I've TA-ed for in Berkeley, and it combines volumes, related rates, and the Fundamental Theorem of Calculus! It's the ultimate Calculus 1 Problem!!! Yeah, this is Berkeley-style, but still a really fun problem…

In this video, I'll present a super quick way of calculating the volume of an ellipsoid using determinants, and then I'll explain why there's a Jacobian in the usual multivariable calculus change of variables formula. Witness again the power of linear algebra

In this video I calculate the Jordan canonical form of a 3x3 matrix by presenting all the 3 cases that could occur. This approach is a bit nontraditional and is a bit longer than the usual approach, but it works most of the time is (in my opinion) easier…

You may be familiar with derivatives, but do you know how to take half-derivatives? What does that even mean? In this video I define the concept of a half derivative, and then calculate the half-derivative of x^n, and then show what that result is for x.…

In this video, I give the classical proof of the fundamental theorem of calculus, the version which says that the derivative of the integral is just the function itself (this is sometimes called FTC 1). There are some epsilon-deltas involved, but not too…

If you ever want to impress someone on a math date, this is the thing you should present! It's basically integration by parts but really quick, and provides a super quick way of integrating a polynomial times a function. Use it for example when you calculate…

In this video I present the second derivative test in multivariable calculus, which is used to find local maxima/minima/saddle points of a function. However, unlike the nonsense they usually teach in the books, here I'm presenting a more elegant way with…

0,1,0,1,0,1,... https://www.youtube.com/watch?v=OOzPXSfu_mc 0,0,1,0,0,1,... https://www.youtube.com/watch?v=p2nznXSXZMY repeating sequence, math for fun, bla...

just for fun with my students & viewers, how NOT to add fractions, Faray addition, math for fun, blackpenredpen,

Here's the problem: https://www.youtube.com/watch?v=0qxBpBypHEg , blackpenredpen, math for fun,

Ostrogradsky method, or "Ostrogradski" according to https://www.encyclopediaofmath.org/index.php/Ostrogradski_method ,
integral of 1/(1+x^2)^2,
rare integration technique,
via trig substitution, https://www.youtube.com/watch?v=DmdWIWSH904 ,
integral…

Jian's github: https://github.com/Crolabear/record1/blob/master/steveBoringFraction.txt , multi-step fraction addition problems, my kind of number theory, te...

integral of 1/(1+x^2)^2,
integral of 1/(x^2+1)^2,
integral battle,


math for fun,
blackpenredpen,

Check out more calculus lessons on Brilliant: https://brilliant.org/blackpenredpen/ , first 200 people to sign up will get 20% off.

How to evaluate the limit of (n!/n^)^(1/n) as n approaches infinity. This limit problem will turn into a Riemann sum and…

a story in my calc 2 class,
阿胡 solved a problem that I didn't try hard to solve since 2015.

blackpenredpen,
math for fun,


find a recursive formula of a sequence,
find a recurrent formula of a sequence,
find an explicit formula of a sequence,
calculus…

0,0,0,1,0,0,0,1,... my subscriber's formula, faster & better,
sequence,

0,1,0,1,0,1,... https://www.youtube.com/watch?v=OOzPXSfu_mc
0,0,1,0,0,1,... https://www.youtube.com/watch?v=p2nznXSXZMY
repeating sequence,


math for fun,
blackpenredpen,

Evaluate the limit of x^x^x as x goes to 0+
0^0 goes to 1, https://www.youtube.com/watch?v=hjEwb-zfJFM ,
0^0 goes to e, https://www.youtube.com/watch?v=zyQtN7Zbi-c ,
0^0 goes to 0, https://www.youtube.com/watch?v=Gcl_9KIdpso ,

🔑 If you enjoy my videos…

fake solution, extraneous solution, solve rational equations, creating a rational equation with fake a solution, math for fun, blackpenredpen,

another logic/math puzzle! blackpenredpen, math for fun,