Solution Found!
Any methoda. Use any analytical method to find
Chapter 8, Problem 59E(choose chapter or problem)
Any method
a. Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. In most cases you do not need to use the definition of the Taylor series coefficients.
b. If possible, determine the radius of convergence of the series.
\(f(x)=\frac{1}{x^{4}+2 x^{2}+1}\)
Questions & Answers
QUESTION:
Any method
a. Use any analytical method to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. In most cases you do not need to use the definition of the Taylor series coefficients.
b. If possible, determine the radius of convergence of the series.
\(f(x)=\frac{1}{x^{4}+2 x^{2}+1}\)
ANSWER:Solution 59E
Step 1:
a) In this problem we need to find the first four nonzero terms of the taylor series centered at ‘0’ for the function f(x) = by using the taylor series :
We know that , , for -1 < x < 1
Consider , =
, since
=
By , using for -1 < x< 1 ,we get
= 1 -2(
)+3
, for -1 <
< 1
= 1 -2+3
,for -1 <
< 1
Therefore , the first four nonzero terms of the taylor series centered at ‘0’ for the function are 1 -2
+3
.
That is , 1, - 2 , 3
,
.
First term = 1
Second term = - 2
Third term = 3
Fourth term =