Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises: 24

Answer

$\lim\limits_{x \to - \infty}(1.001)^{x}=0$

Work Step by Step

Evaluate limit for $\lim\limits_{x \to - \infty}(1.001)^{x}$ Consider $(1.001) =t$ Since $t\gt1$ $\lim\limits_{x \to - \infty}(1.001)^{x}=\lim\limits_{x \to -\infty}t^{x} ; t>1$ This implies $1.001>1$ Hence, $\lim\limits_{x \to - \infty}(1.001)^{x}=0$
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