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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
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 $x = 0$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d) $\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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