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Question Number 115384 by mathdave last updated on 25/Sep/20

$$solvethelimitproblem$$$$\underset{x\to \mathrm{\infty }}{\lim }\left(\frac{\cos x}{1-e^{-x}}\right)$$

Answered by MJS_new last updated on 25/Sep/20

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{\cos x}{1-{\mathrm{e}}^{-x}}=\underset{x\to \mathrm{\infty }}{\lim }\frac{{\mathrm{e}}^x}{{\mathrm{e}}^x-1}\cos x=\underset{x\to \mathrm{\infty }}{\lim }\cos x$$$$\Rightarrow \mathrm{limit}{\mathrm{doesn}}^{\prime }\mathrm{t}\mathrm{exist}$$

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