lim _{x rightarrow frac{pi}{2}} left(frac{2x- | vedclass

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(C) Let $\ell = \lim _{x \rightarrow \frac{\pi}{2}} \frac{2x-\pi}{\cos x}$.This is an indeterminate form of type $\frac{0}{0}$.Applying $L$' Hospital'

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$-2$

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(C) Let $\ell = \lim _{x \rightarrow \frac{\pi}{2}} \frac{2x-\pi}{\cos x}$.This is an indeterminate form of type $\frac{0}{0}$.Applying $L$' Hospital's rule by differentiating the numerator and denominator with respect to $x$:$\ell = \lim _{x \rightarrow \frac{\pi}{2}} \frac{\frac{d}{dx}(2x-\pi)}{\frac{d}{dx}(\cos x)}$$\ell = \lim _{x \rightarrow \frac{\pi}{2}} \frac{2}{-\sin x}$Substituting $x = \frac{\pi}{2}$:$\ell = \frac{2}{-\sin(\frac{\pi}{2})} = \frac{2}{-1} = -2$.

$\lim _{x \rightarrow \frac{\pi}{2}} \left(\frac{2x-\pi}{\cos x}\right)$ is equal to

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