Findlim-x-0-e-1-x-1-e-1-x-1-

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Question Number 379 by userid1 last updated on 25/Jan/15

$$\mathrm{Find}\underset{x\to 0}{\lim }\left(\frac{e^{1/x}-1}{e^{1/x}+1}\right)$$

Commented by 123456 last updated on 25/Dec/14

$$\underset{x\to 0+}{\lim }\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}\stackrel{?}{=}\underset{x\to 0+}{\lim }\frac{-\frac{1}{x^2}{e}^{\frac{1}{x}}}{-\frac{1}{x^2}{e}^{\frac{1}{x}}}\stackrel{?}{=}1(\to \frac{\mathrm{\infty }}{\mathrm{\infty }})$$$$\underset{x\to 0-}{\lim }\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}\stackrel{?}{=}\frac{0-1}{0+1}\stackrel{?}{=}-1$$$$\underset{x\to 0}{\lim }\frac{e^{\frac{1}{x}}-1}{e^{\frac{1}{x}}+1}\stackrel{?}{=}\nexists$$

Answered by prakash jain last updated on 27/Dec/14

$$\mathrm{A}s\mathrm{given}\mathrm{in}\mathrm{comments}\mathrm{for}\mathrm{given}\mathrm{function}$$$$\underset{x\to 0^{+}}{\lim }f\left(x\right)\ne \underset{x\to 0^{-}}{\lim }f\left(x\right)$$$$\mathrm{so}\mathrm{the}\mathrm{limit}\mathrm{is}\mathrm{not}\mathrm{defined}$$

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