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,

Story with my students, Dear Paul, square root equations, square both side, blackpenredpen, math for fun,

integral of 1/(x*(1+x^2)^2),
integral of 1/((1+x^2)^2),
integral by partial fraction,
integral by trig sub,
partial fraction with repeated quadratic factors,
Partial fraction vs. Trig sub


blackpenredpen,
math for fun,

what is 0 to the 0th power? , Can the 0^0 approach to 0, 0^0 goes to 1, https://www.youtube.com/watch?v=hjEwb-zfJFM , 0^0 goes to e, https://www.youtube.com/...