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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
MCQ
$\lim _{x \rightarrow a} \frac{\cos x-\cos a}{\cot x-\cot a}=$
  • A
    $\frac{1}{2} \sin ^3 a$
  • B
    $\frac{1}{2} \operatorname{cosec}^3 a$
  • ✓
    $\sin ^3 a$
  • D
    $\operatorname{cosec}^3 a$
✓

Answer

Correct option: C.
$\sin ^3 a$
(C)
Applying L Hospital’s Rule, we get
$\lim _{x \rightarrow a} \frac{\cos x-\cos a}{\cot x-\cot a}=\lim _{x \rightarrow a}\left(\frac{-\sin x}{-\operatorname{cosec}^2 x}\right)$
$=\lim _{x \rightarrow a } \sin ^3 x=\sin ^3 a$

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