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The Taylor Series


Problems 4

Summary Problems 4

Problem : Prove that (sin(x)) = cos(x) using the Taylor series of the two functions.


sin(x) = x2n+1    

has infinite radius of convergence, we can differentiate term-by-term:


Problem : Prove that 1/(x + 1)dx = log(x + 1) using Taylor series. (The Taylor series for 1/(x + 1) is (- 1)nxn.)

We have

dx=(- 1)nxndx