Question

What is the limit of title=" \frac{1- e^{x} }{1+2e^x} " alt=" \frac{1- e^{x} }{1+2e^x} " align="absmiddle" class="latex-formula"> as x approaches infinity. Steps PLEASE.

Answer 1

Hello,

$\lim_{x \to \infty} \dfrac{1-e^x}{1+2e^x}\\ = \lim_{x \to \infty} \dfrac{ \dfrac{1-e^x}{e^x}}{ \dfrac{1+2e^x}{e^x}}\\ = \lim_{x \to \infty} \dfrac{ \dfrac{1}{e^x}-1}{\dfrac{1}{e^x}+2}\\ = \dfrac{0-1}{0+2} =- \dfrac{1}{2}$