Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - 6.4* General Logarithmic and Exponential Functions - 6.4* Exercise: 21

Answer

$\lim\limits_{x \to \infty}(1.001)^{x}=\infty$

Work Step by Step

Evaluate limit for $\lim\limits_{x \to \infty}(1.001)^{x}$ $\lim\limits_{x \to \infty}(1.001)^{x}=\lim\limits_{x \to \infty} e^{ln(1.001)^{x}}$ $=\lim\limits_{x \to \infty} e^{x ln(1.001)}$ Consider $t=xln(1.001)$ $\lim\limits_{x \to \infty} xln(1.001)=\lim\limits_{t \to\infty }t$ Thus, $\lim\limits_{x \to \infty} e^{x ln(1.001)}=\lim\limits_{t \to \infty}e^{t}=\infty$ Hence, $\lim\limits_{x \to \infty}(1.001)^{x}=\infty$
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