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Solved: Exponential function In Section 9.3, we show that
Chapter 8, Problem 60E(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.
\(f(x)=e^{2 x}\)
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.
\(f(x)=e^{2 x}\)
ANSWER:Solution 60E
Step 1:
We are given that for