LetT10x be the taylor polynomial of degree 10 of the functio

LetT10(x): be the taylor polynomial of degree 10 of the functionf(x)=ln(1+x)ata=0.
Suppose you approximate f(x)byT10(x), find all positive values ofxfor which this approximation is

Solution

T = x - x^2/2 + x^3/3 - .. -x^10/10
Error term is approx x^11/11 ~ 0.001
This approximation is within 0.001 of the right answer
when0< x <= 0.6636