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  • <img alt="\mathrm{\lim _{x \rightarrow \pi} \frac{\cos ^{-1}(\cos x)-\pi}{\sin ^{-1}(\sin x)} \text { is equal to }}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Clim%20_%7Bx

\mathrm{\lim _{x \rightarrow \pi} \frac{\cos ^{-1}(\cos x)-\pi}{\sin ^{-1}(\sin x)} \text { is equal to }}

Option: 1

-1


Option: 2

1


Option: 3

does not exists
 


Option: 4

none of these


Answers (1)

\mathrm{\begin{aligned} \mathrm{LHL} & =\lim _{x \rightarrow \pi^{-}} \frac{\cos ^{-1}(\cos x)-\pi}{\sin ^{-1}(\sin x)}=\frac{x-\pi}{\pi-x}=-1 \\\\ \mathrm{RHL} & =\lim _{x \rightarrow \pi^{+}} \frac{\cos ^{-1}(\cos x)-\pi}{\sin ^{-1}(\sin x)}=\frac{2 \pi-x-\pi}{\pi-x}=1 \end{aligned}}

Hence the limit does not exists.

 

Posted by

Kshitij

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