lim ( x tends to 0) e^1/x / e^1/x+1

\lim_{x \to 0} \frac{e^{\frac{1}{x}}}{e^{\frac{1}{x} + 1}} = \lim_{x \to 0} \frac{e^{\frac{1}{x}}}{e^{\frac{1}{x}} . e^{1}} Now e^{\frac{1}{x}} will be get cancelled, = \lim_{x \to 0} \frac{1}{e} = \frac{1}{e}

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lim ( x tends to 0) e1/x / e1/x+1