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5. continuity and differentiation — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths5. continuity and differentiation1 Mark
MCQ
If $f(x) = \left\{ {\begin{array}{*{20}{c}}  {\frac{{\sin x}}{x} + \cos x,} \, & \,when \,\, {x \ne 0} \\   {2,} \,& \,\,when\,\,{x = 0} \end{array}} \right.$  then 
  • A
    $\mathop {\lim }\limits_{x \to 0 + } f(x) \ne 2$
  • B
    $\mathop {\lim }\limits_{x \to 0 - } f(x) = 0$
  • ✓
    $f(x)$ is continuous at $ x = 0$
  • D
    None of these
✓

Answer

Correct option: C.
$f(x)$ is continuous at $ x = 0$
c
(c) $ f(0 + ) = f(0 - ) = 2$ and $f(0) = 2$

Hence $f(x)$ is continuous at $x = 0.$

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