Two Pwr Series Questions- relatively simple

[asif zaidi]

Hello:
(at least I think they are simple !)

The 1st question is not a h/w problem. It is a question from textbook
The 2nd question is a h/w problem.

Problem1:
The series for log(1+x) is proven -1<x<=1. It then says the Taylor Series for (1/x)log(1+x) follows.
Do they mean that the individual components of log(1+x) will be multiplied by (1/x). If true, would this apply for x, x^2 etc...

Problem2:
Put e=exp(1). Use the Taylor Series expansion of exp to compute e.

Solution
When I solve this, I can get the TS for exp. Do I have to evaluate it at x=1?

Thanks

Asif

 

[Dick]

For the first one, if by components you mean power series terms, yes. For the second, yes, you have to put x=1 in. How many terms you need to keep depends on the accuracy of the answer you need. You'll need a taylor series remainder term if you need to be rigorous about it.