What is the limit of \(\frac{1- e^{x} }{1+2e^x}\) as x approaches infinity. Steps PLEASE.

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14-09-2016
Mathematics

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What is the limit of \(\frac{1- e^{x} }{1+2e^x}\) as x approaches infinity. Steps PLEASE.

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caylus caylus · Answer 1 · 2016-09-14T12:49:55-04:00

caylus caylus

14-09-2016

Hello,

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

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