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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
The value of $k$ which makes $f(x) = \left\{ \begin{array}{l}\sin \frac{1}{x},\;x \ne 0\\\,\,\,\,\,\,\,\,k,\,x = 0\end{array} \right.$ continuous at $x = 0$ is
  • A
    $8$
  • B
    $1$
  • C
    $-1$
  • ✓
    None of these
✓

Answer

Correct option: D.
None of these
d
(d) If $x \to 0,$ then the value of $\sin \frac{1}{x}$ passes through $[-1, 1]$ infinitely many ways,

therefore limit of the function does 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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