Iff(x) = l e^ 1/x , ; when ;x 0 0, ; ; ; ; ; when ;x = 0 ., then - Vidyadip

MCQ

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

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

✓

Answer

$f(0) = 0$
$\mathop {\lim }\limits_{x \to 0 - } f(x) = \mathop {\lim }\limits_{h \to 0} \,{e^{ - 1/h}} = 0$
and $\mathop {\lim }\limits_{x \to 0 + } f(x) = \mathop {\lim }\limits_{h \to 0} \,{e^{1/h}} = \infty $
Hence function is discontinuous at $x = 0.$

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