mathop {lim }limits_{x to a} frac{{cos x - co | vedclass

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(C) Given the limit: $\mathop {\lim }\limits_{x 	o a} \frac{{\cos x - \cos a}}{{\cot x - \cot a}}$Applying $L$'$H$ôpital's Rule by differentiating th

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$\sin ^3 a$

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(C) Given the limit: $\mathop {\lim }\limits_{x 	o a} \frac{{\cos x - \cos a}}{{\cot x - \cot a}}$Applying $L$'$H$ôpital's Rule by differentiating the numerator and denominator with respect to $x$:Numerator: $\frac{d}{dx}(\cos x - \cos a) = -\sin x$Denominator: $\frac{d}{dx}(\cot x - \cot a) = -\csc^2 x$Thus,the limit becomes: $\mathop {\lim }\limits_{x 	o a} \frac{-\sin x}{-\csc^2 x} = \mathop {\lim }\limits_{x 	o a} \frac{\sin x}{\frac{1}{\sin^2 x}} = \mathop {\lim }\limits_{x 	o a} \sin^3 x$Evaluating the limit as $x 	o a$: $\sin^3 a$.

$\mathop {\lim }\limits_{x \to a} \frac{{\cos x - \cos a}}{{\cot x - \cot a}} = $

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