Answer 2 Taylor Series Questions to Earn Best Answer!?

Question

1) Consider the following function: f(x)= 1/x

A) Find the first four nonzero terms of the Taylor series fro the given function about -2. You will need to convert any factorials into integers.
1st Term:
2nd Term:
3rd Term:
4th Term:

B) Find an expression for the general term of the Taylor series assuming the starting value of the index, k is 0.


2) Consider the following function: f(x)= 1/(1-x)

A) Find the first four nonzero terms of the Taylor series fro the given function about 0. You will need to convert any factorials into integers.
1st Term:
2nd Term:
3rd Term:
4th Term:

B) Find an expression for the general term of the Taylor series assuming the starting value of the index, k is 0.

Answer 1

1. A) 1/2 -(x - 2)/4 +(x - 2)^2/8 - 3(x - 2)^3/48 + ...

B) f^(k)(2)*(x - 2)^k/k!

2. A) 1 + x + x^2 + x^3 + ...
B) x^k