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STD 11 - 12. limits — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 12. limits4 Marks
MCQ
$\mathop {\lim }\limits_{x \to a} \frac{{\cos x - \cos a}}{{\cos x - \cot a}} = $
  • A
    $\frac{1}{2}{\sin ^3}a$
  • B
    $\frac{1}{2}{\rm{cose}}{{\rm{c}}^2}a$
  • ✓
    ${\sin ^3}a$
  • D
    ${\rm{cose}}{{\rm{c}}^3}a$
✓

Answer

Correct option: C.
${\sin ^3}a$
c
(c) $\mathop {\lim }\limits_{x \to a} \,\frac{{\cos x - \cos a}}{{\cot x - \cot a}} = \mathop {\lim }\limits_{x \to a} \,\left( {\frac{{ - \sin x}}{{ - \cos e{c^2}x}}} \right) $

$= \mathop {\lim }\limits_{x \to a} {\sin ^3}x = {\sin ^3}a$.

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