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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 $f(x) = \left\{ \begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,x\sin x,\,{\rm{when \,\,}}0 < x \le \frac{\pi }{2}\\\frac{\pi }{2}\sin (\pi + x),{\rm{when\,\,}}\frac{\pi }{{\rm{2}}} < x < \pi \end{array} \right.$, then
  • ✓
    $f(x)$ is discontinuous at $x = \pi /2$
  • B
    $f(x)$ is continuous at $x = \pi /2$
  • C
    $f(x)$ is continuous at $x = 0$
  • D
    None of these
✓

Answer

Correct option: A.
$f(x)$ is discontinuous at $x = \pi /2$
a
$\mathop {\lim }\limits_{x \to \frac{\pi }{{{2^ - }}}} \,f(x) = \frac{\pi }{2}, \,\, \mathop {\lim }\limits_{x \to \frac{\pi }{{{2^ + }}}} f(x) = \frac{{ - \pi }}{2}$

and $f\left( {\frac{\pi }{2}} \right) = \frac{\pi }{2}.$

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