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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
The function $\frac{\sin x}{|x|}$
  • A
    is continuous at $x=0$
  • ✓
    is discontinuous at $x=0$
  • C
    has removable discontinuity at $x=0$
  • D
    none of these
✓

Answer

Correct option: B.
is discontinuous at $x=0$
(B)
$\lim _{x \rightarrow 0^{+}} \frac{\sin x}{|x|}=\lim _{x \rightarrow 0} \frac{\sin x}{x}=1$
and $\lim _{x \rightarrow 0^{-}} \frac{\sin x}{|x|}=\lim _{x \rightarrow 0} \frac{\sin x}{-x}=-1$
∴ the given function is discontinuous at $x=0$.

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