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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
The value of k which makes $f(x)=\left\{\begin{array}{c}\sin \frac{1}{x}, x \neq 0 \\ k , x=0\end{array}\right.$ continuous at $x=0$ is
  • A
    8
  • B
    1
  • C
    -1
  • ✓
    none of these
✓

Answer

Correct option: D.
none of these
(D) If $x \rightarrow 0$, then the value of $\sin \frac{1}{x}$ passes through $[-1,1]$ infinitely many ways, therefore, limit of the function docs not exist at $x=0$. Hence, there is no value of k for which the function is continuous at $x=0$.

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