Solution Found!
Answer: Exponential function In Section 9.3, we show that
Chapter 8, Problem 61E(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.
\(f(x)=e^{-3 x}\)
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.
\(f(x)=e^{-3 x}\)
ANSWER:Solution 61EStep 1:We are given that for We have to find the power series for To find th