_ x 0 + x e^ 1/x 1 + e^ 1/x = - Vidyadip

MCQ

$\mathop {\lim }\limits_{x \to 0 + } \frac{{x{e^{1/x}}}}{{1 + {e^{1/x}}}} = $

✓
$0$
B
$1$
C
$\infty $
D
None of these

✓

Answer

Correct option: A.

$0$

a
(a) $\mathop {\lim }\limits_{x \to 0 + } \frac{x}{{1 + {e^{ - 1/x}}}} = 0$

as ${e^{ - 1/x}} \to 0$ when $x \to {0^ + }$

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