If mathop {lim }limits_{x to 0} kx,text{cosec | vedclass

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(C) Given: $\mathop {\lim }\limits_{x 	o 0} kx\,	ext{cosec}\,x = \mathop {\lim }\limits_{x 	o 0} x\,	ext{cosec}\,kx$We know that $	ext{cosec}\,

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$\pm 1$

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(C) Given: $\mathop {\lim }\limits_{x 	o 0} kx\,	ext{cosec}\,x = \mathop {\lim }\limits_{x 	o 0} x\,	ext{cosec}\,kx$We know that $	ext{cosec}\,	heta = \frac{1}{\sin 	heta}$.So,$\mathop {\lim }\limits_{x 	o 0} \frac{kx}{\sin x} = \mathop {\lim }\limits_{x 	o 0} \frac{x}{\sin kx}$Multiply and divide the right side by $k$: $\mathop {\lim }\limits_{x 	o 0} \frac{kx}{\sin x} = \frac{1}{k} \mathop {\lim }\limits_{x 	o 0} \frac{kx}{\sin kx}$Using the standard limit $\mathop {\lim }\limits_{	heta 	o 0} \frac{	heta}{\sin 	heta} = 1$,we get:$k(1) = \frac{1}{k}(1)$$k = \frac{1}{k}$$k^2 = 1$$k = \pm 1$

If $\mathop {\lim }\limits_{x \to 0} kx\,\text{cosec}\,x = \mathop {\lim }\limits_{x \to 0} x\,\text{cosec}\,kx$,then $k = $

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