limx→∞ 1+kxmx is equal to

$lim_{x \to \infty} {(1 + \frac{k}{x})}^{m x}$ is equal to

A
$m^{k}$
B
$e^{m}$
C
$e^{m k}$
D
$e^{m / k}$

Solution:

$lim_{x \to \infty} {(1 + \frac{k}{x})}^{m x} = lim_{k \to \infty} {(1 + \frac{k}{x})}^{\frac{x}{k} \cdot m k} = e^{m k}$ .

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