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

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

Answer

Correct option: B.
$f(x)$  is discontinuous at $x = 0$
b
(b) $\mathop {\lim }\limits_{x \to 0 - } f(x) = 1 + 1 = 2,\,\,\mathop {\lim }\limits_{x \to 0 + } f(x) = 0,\,\,f(0) = 2$.

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