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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow 0} \frac{\sin (2+x)-\sin (2-x)}{x}=$
  • A
    $\sin 2$
  • B
    $2 \sin 2$
  • ✓
    $2 \cos 2$
  • D
    2
✓

Answer

Correct option: C.
$2 \cos 2$
(C)
$\lim _{x \rightarrow 0} \frac{\sin (2+x)-\sin (2-x)}{x}=\lim _{x \rightarrow 0} \frac{2 \cos 2 \cdot \sin x}{x}$
$=2 \cos 2 \lim _{x \rightarrow 0} \frac{\sin x}{x}$
$=2 \cos 2$

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