Chapter 6 - Inverse Functions - 6.2 Exponential Functions and Their Derivatives - 6.2 Exercises - Page 418: 24

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

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