If f(x) = l 2^ 1/x , for , , ,x 0 , , , , , , ,3, for , , ,x = 0 … - Vidyadip

MCQ

If $f(x) = \left\{ \begin{array}{l}{2^{1/x}},{\rm{for\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,3,{\rm{for\,\,}}\,x = {\rm{0}}\end{array} \right.$, then

A
$\mathop {\lim }\limits_{x \to 0 + } f(x) = 0$
B
$\mathop {\lim }\limits_{x \to 0 - } f(x) = \infty $
C
$f(x)$ is continuous at $x = 0$
D
None of these

✓

Answer

$\mathop {\lim }\limits_{x \to 0 + } f(x) = \mathop {\lim }\limits_{h \to 0} \,\,{2^{1/h}} = \infty $
$\mathop {\lim }\limits_{x \to 0 - } f(x) = \mathop {\lim }\limits_{h \to 0} \,\,{2^{ - 1/h}} = \mathop {\lim }\limits_{h \to 0} \,\frac{1}{{{2^{1/h}}}} = 0$.

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