_ x ( 1 + 2 x )^x = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + \frac{2}{x}} \right)^x} = $

A
$e$
B
$\frac{1}{e}$
✓
${e^2}$
D
None of these

✓

Answer

Correct option: C.

${e^2}$

c
(c)${\left[ {\mathop {\lim }\limits_{x \to \infty } {{\left( {1 + \frac{1}{{x/2}}} \right)}^{x/2}}} \right]^2} = {e^2}.$

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