Match the items given under List I with the items given under List II

	List I		List II
1)	$\underset{x\to \frac{\pi }{2}}{\lim }\frac{(\frac{\pi }{2}-x)\sin x-2\cos x}{(\frac{\pi }{2}-x)+\cot x}=$	i)	-1
2)	$2^{1/4}\underset{x\to \frac{\pi }{4}}{\lim }\frac{\sqrt{\cos x}-\sqrt{\sin x}}{x-\pi /4}=$	ii)	1/4
3)	$8\underset{x\to \frac{\pi }{8}}{\lim }\frac{\cot 4x-\cos 4x}{{(\pi -8x)}^3}=$	iii)	-1/2
4)	$\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sqrt{2-\sin x}-1}{{(\frac{\pi }{2}-x)}^2}=$	iv)	1/2

A)  $\underset{x\to \frac{\pi }{2}}{\lim }\frac{(\frac{\pi }{2}-x)\sin x-2\cos x}{(\frac{\pi }{2}-x)+\cot x}=\underset{x\to \frac{\pi }{2}}{\lim }\frac{\sin x-2\frac{\sin (\frac{\pi }{2}-x)}{(\frac{\pi }{2}-x)}}{1+\frac{\tan (\frac{\pi }{2}-x)}{(\frac{\pi }{2}-x)}} =\frac{1-2}{1+1}=-\frac{1}{2}$

B) $2^{1/4}\underset{x\to \pi /4}{\lim }\frac{\sqrt{\cos x}-\sqrt{\sin x}}{x-\pi /4}$$=2^{1/4}\underset{x\to \pi /4}{\lim }\frac{\cos x-\sin x}{x-\pi /4}\frac{1}{\sqrt{\cos x}+\sqrt{\sin x}}$

$=-2^{1/4}\sqrt{2}\underset{x\to \pi /4}{\lim }\frac{\sin (x-\pi /4)}{x-\pi /4}\frac{1}{2\sqrt{\frac{1}{\sqrt{2}}}}=-1$

C)  $L=8\underset{x\to \frac{\pi }{8}}{\lim }\frac{\cot 4x-\cos 4x}{{(\pi -8x)}^3} Put 8x-\pi =t$

$$\begin{gathered} \therefore L=8\underset{t\to 0}{\lim }\frac{\cos (\frac{\pi }{2}+\frac{t}{2})(1-\sin (\frac{\pi }{2}+\frac{t}{2}))}{-t^3} =8\underset{t\to 0}{\lim }\frac{\sin \frac{t}{2}(1-\cos \frac{t}{2})}{t^3} \\ =8\underset{t\to 0}{\lim }\frac{1-\cos \frac{t}{2}}{2t^2}=8\underset{t\to 0}{\lim }\frac{{\sin }^2\frac{t}{4}}{t^2}=\frac{1}{2} \end{gathered}$$