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14-09-2016
Mathematics

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What is the limit of [tex] \frac{1- e^{x} }{1+2e^x} [/tex] as x approaches infinity. Steps PLEASE.

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14-09-2016

Hello,

[tex] \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} [/tex]

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