Solution Found!
Exponential function In Section 9.3, we show that the
Chapter 8, Problem 59E(choose chapter or problem)
Exponential function In Section 9.3, we show that the power series for the exponential function centered at 0 is
\(e^{x}=\sum_{k=0}^{\infty} \frac{x^{k}}{k !}\), for \(-\infty<x<\infty\).
Use the methods of this section to find the power series for the following functions. Give the interval of convergence for the resulting series.
\(f(x)=e^{-x}\)
Questions & Answers
QUESTION:
Exponential function In Section 9.3, we show that the power series for the exponential function centered at 0 is
\(e^{x}=\sum_{k=0}^{\infty} \frac{x^{k}}{k !}\), for \(-\infty<x<\infty\).
Use the methods of this section to find the power series for the following functions. Give the interval of convergence for the resulting series.
\(f(x)=e^{-x}\)
ANSWER:Solution 59EStep 1:We have the power series representationWith the interval of convergence (-