Solution Found!
Solution: Any methoda. Use any analytical method to find the
Chapter 8, Problem 55E(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.
\(f(x)=\left(1+x^{2}\right)^{-2 / 3}\)
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.
\(f(x)=\left(1+x^{2}\right)^{-2 / 3}\)
ANSWER:Solution 55EStep 1:We know the taylor series of For and , we substitute in place of x and Hence the new taylor series becomes,Therefore the first four nonzero terms of the new series are: .