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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow \alpha} \frac{\sin x-\sin \alpha}{x-\alpha}=$
  • A
    $0$
  • B
    1
  • C
    $\sin \alpha$
  • ✓
    $\cos \alpha$
✓

Answer

Correct option: D.
$\cos \alpha$
(D)
Applying L-Hospital's rule, we get
$\lim _{x \rightarrow \alpha} \frac{\sin x-\sin \alpha}{x-\alpha}=\lim _{x \rightarrow \alpha} \frac{\cos x}{1}=\cos \alpha$

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