my all-in-one calculus question (uncut)

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Here's another all-in-one ultimate calculus question that I came up with! We have the first principle limit definition of derivative of 1/x^2, then the power rule, followed by an infinite geometric series and we will end with an integral with partial fraction decompositions. This is an integral of an infinite series of the derivative of the limit of a difference quotient! I would say this is an ultimate calculus question for the final exam! Free feel to use this for your class if you are also a calculus teacher! #calculus #blackpenredpen

If you like this video, then you should watch this video next: "when d/dx(x^2) becomes the hardest question on your calculus final" 👉    • calc 1 final be like (derivative of x^2)  

0:00 limit definition of derivative of 1/x^2
2:20 derivative by using the power rule
2:58 infinite geometric series
5:17 partial fraction decomposition with quadratic denominators
10:54 the actual integration
14:12 integral of 1/(1-x^2) is coth^-1(x) when abs(x) is greater than 1
*How to integrate 1/(1-x^2):    • the integral of 1/(1-x^2) (hyperbolic...  *
16:16 WOW!
17:18 Check out Brilliant

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