limx→x 1+2xx equals

$lim_{x \to x} {(1 + \frac{2}{x})}^{x}$ equals

A
$e$
B
$\infty$
C
$e^{2}$
D
$\frac{1}{e}$

Solution:

We have,

$lim_{x \to \infty} {(1 + \frac{2}{x})}^{x} = e^{lim_{x \to \infty} \frac{2}{x} \times x} = e^{2}$

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