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STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If $f(x) = \left\{ \begin{array}{l}\frac{{x - |x|}}{x},{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,\,2,\,{\rm{when}}\,\,x = 0\end{array} \right.,$ then
  • A
    $f(x)$ is continuous at $x = 0$
  • B
    $f(x)$  is discontinuous at $x = 0$
  • C
    $\mathop {\lim }\limits_{x \to 0} f(x) = 2$
  • D
    None of these
✓

Answer

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

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