यदि mathop {lim }limits_{x to 0} kx,text{cose | vedclass

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(C) दिया गया है: $\mathop {\lim }\limits_{x 	o 0} kx\,	ext{cosec}\,x = \mathop {\lim }\limits_{x 	o 0} x\,	ext{cosec}\,kx$हम जानते हैं कि $	ext{c

Vedclass · Accepted Answer

$\pm 1$

Vedclass · Answer

(C) दिया गया है: $\mathop {\lim }\limits_{x 	o 0} kx\,	ext{cosec}\,x = \mathop {\lim }\limits_{x 	o 0} x\,	ext{cosec}\,kx$हम जानते हैं कि $	ext{cosec}\,	heta = \frac{1}{\sin 	heta}$ होता है।अतः,$\mathop {\lim }\limits_{x 	o 0} \frac{kx}{\sin x} = \mathop {\lim }\limits_{x 	o 0} \frac{x}{\sin kx}$दाहिनी ओर $k$ से गुणा और भाग करने पर: $\mathop {\lim }\limits_{x 	o 0} \frac{kx}{\sin x} = \frac{1}{k} \mathop {\lim }\limits_{x 	o 0} \frac{kx}{\sin kx}$मानक सीमा $\mathop {\lim }\limits_{	heta 	o 0} \frac{	heta}{\sin 	heta} = 1$ का उपयोग करने पर:$k(1) = \frac{1}{k}(1)$$k = \frac{1}{k}$$k^2 = 1$$k = \pm 1$

यदि $\mathop {\lim }\limits_{x \to 0} kx\,\text{cosec}\,x = \mathop {\lim }\limits_{x \to 0} x\,\text{cosec}\,kx$ है,तो $k = $

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