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STD 12 - 5. continuity and differentiation — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ \begin{array}{l}{\sin ^{ - 1}}|x|,{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,{\rm{when\,\, }}x = 0\end{array} \right.$ then
  • A
    $\mathop {\lim }\limits_{x \to 0 + } f(x) \ne 0$
  • B
    $\mathop {\lim }\limits_{x \to 0 - } f(x) \ne 0$
  • ✓
    $f(x)$ is continuous at $x = 0$
  • D
    None of these
✓

Answer

Correct option: C.
$f(x)$ is continuous at $x = 0$
c
(c) $\mathop {\lim }\limits_{x \to 0} \,\,f(x) = {\sin ^{ - 1}}(0) = 0$ and $f(0) = 0$

Hence $f(x)$ is continuous at $x = 0.$

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