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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}{(1 + 2x)^{1/x}},\,{\rm{for\,\, }}x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{e^2},\,{\rm{for\,\, }}x = 0\,\,\,\end{array} \right.$, then
  • A
    $\mathop {\lim }\limits_{x \to 0 + } f(x) = e$
  • ✓
    $\mathop {\lim }\limits_{x \to 0 - } f(x) = {e^2}$
  • C
    $f(x)$ is discontinuous at $x = 0$
  • D
    None of these
✓

Answer

Correct option: B.
$\mathop {\lim }\limits_{x \to 0 - } f(x) = {e^2}$
b
(b) $\mathop {\lim }\limits_{x \to 0 - } f(x) = \mathop {\lim }\limits_{x \to 0} \,\,{\left[ {{{(1 + 2x)}^{1/2x}}} \right]^2} = {e^2}.$

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