Solution Found!
Working with binomial series Use properties of
Chapter 8, Problem 39E(choose chapter or problem)
Working with binomial series Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. Give the interval of convergence for the new series. Use the Taylor series
\(\sqrt{1+x}=1+\frac{x}{2}-\frac{x^{2}}{8}+\frac{x^{3}}{16}-\cdots\), for \(-1<x \leq 1\).
\(\sqrt{a^{2}+x^{2}}, a>0\)
Questions & Answers
QUESTION:
Working with binomial series Use properties of power series, substitution, and factoring to find the first four nonzero terms of the Taylor series centered at 0 for the following functions. Give the interval of convergence for the new series. Use the Taylor series
\(\sqrt{1+x}=1+\frac{x}{2}-\frac{x^{2}}{8}+\frac{x^{3}}{16}-\cdots\), for \(-1<x \leq 1\).
\(\sqrt{a^{2}+x^{2}}, a>0\)
ANSWER:Solution 39EStep 1 :Given and Substituting in the given power series to get the new series , we getTherefore the first four nonzero terms of the new series are: .