limx→x 1+2xx equals

# $\underset{x\to x}{lim} {\left(1+\frac{2}{x}\right)}^{x}$ equals

1. A

$e$

2. B

$\infty$

3. C

${e}^{2}$

4. D

$\frac{1}{e}$

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### Solution:

We have,

$\underset{x\to \mathrm{\infty }}{lim} {\left(1+\frac{2}{x}\right)}^{x}={e}^{\underset{x\to \mathrm{\infty }}{lim} \frac{2}{x}×x}={e}^{2}$

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