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Continuity — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsContinuity2 Marks
MCQ
If $f(x)=\left\{\begin{array}{cc}\frac{1-\cos 4 x}{x^2} & ; \text { when } x<0 \\ a & ; \text { when } x=0 \\ \frac{\sqrt{x}}{\sqrt{(16+\sqrt{x})}-4} & ; \text { when } x>0\end{array}\right.$, is continuous at $x=0$, then the value of ' $a$ ' will be
  • ✓
    8
  • B
    -8
  • C
    4
  • D
    16
✓

Answer

Correct option: A.
8
(A)
Since $f (x)$ is continuous at $x=0$.
$\therefore \quad f (0)=\lim _{x \rightarrow 0^{-}} f (x)$
$\Rightarrow a =\lim _{x \rightarrow 0} \frac{1-\cos 4 x}{x^2}$
$=\lim _{x \rightarrow 0} \frac{2 \sin ^2 2 x}{x^2}$
$=2 \lim _{x \rightarrow 0} \frac{\sin ^2 2 x}{(2 x)^2} \times 4=2 \times 4=8$

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