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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$f(x) = \left\{ \begin{array}{l}\frac{{|x - a|}}{{x - a}},{\rm{when\,\,}}\,x \ne a\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,1,{\rm{when\,\,}}\,x = a\end{array} \right.$,then
  • A
    $f(x)$ is continuous at $x = a$
  • ✓
    $f(x)$ is discontinuous at $x = a$
  • C
    $\mathop {\lim }\limits_{x \to a} f(x) = 1$
  • D
    None of these
✓

Answer

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

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