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STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
If $f(x) = \left\{ \begin{array}{l}\frac{{\sin 2x}}{{5x}},{\rm{when\,\,}}\,x \ne 0\\\,\,\,\,\,\,\,\,\,\,\,\,k,{\rm{when \,\,}}x = 0\end{array} \right.$ is continuous at $x = 0$, then the value of  $ k $ will be
  • A
    $1$
  • B
    $\frac{2}{5}$
  • C
    $ - \frac{2}{5}$
  • D
    None of these
✓

Answer

$\mathop {\lim }\limits_{x \to 0} \,f(x) = \mathop {\lim }\limits_{x \to 0} \frac{{2\sin \,2x}}{{2x\,.\,5}} = \frac{2}{5} = k.$

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