I need a little bit of assistance with the following problem:
Calculate general Taylor Series and the first 3 terms of the Taylor series centered at 2 of the
function
f(x) = ln(x^2 + 2x + 1)
I know the first step would be calculating multiple derivatives as below:
f'(x)=2/(x+1)
f"(x)= -2/(x+1)^2
f"'(x)=4/(x+1)^3
f""(x)= -12/(x+1)^4
f""'(x)=48/(x+1)^5
What would be the next step after doing this? I guess my issue is turning this into a taylor series using the formula.
Best Answer
Hint: Since $f(x)=\log\bigl((x+1)^2\bigr)=2\log(x+1)$, then$$f'(x)=\frac2{x+1}=\frac2{3+(x-2)}=\frac23\cdot\frac1{1+\frac{x-2}3}.$$