lim _{x rightarrow 0} frac{(operatorname{cose | vedclass

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Question

(D) આપણે જાણીએ છીએ કે $\operatorname{cosec} x - \cot x = \frac{1-\cos x}{\sin x} = 	an(x/2)$.વળી,$e^x - e^{-x} \approx 2x$ જ્યારે $x 	o 0$.તેથી,અંશ

Vedclass · Accepted Answer

$4 \sqrt{3}$

Vedclass · Answer

(D) આપણે જાણીએ છીએ કે $\operatorname{cosec} x - \cot x = \frac{1-\cos x}{\sin x} = 	an(x/2)$.વળી,$e^x - e^{-x} \approx 2x$ જ્યારે $x 	o 0$.તેથી,અંશ $	an(x/2) \cdot (e^x - e^{-x}) \approx (x/2) \cdot (2x) = x^2$ થાય.છેદ માટે,$\sqrt{3} - \sqrt{2+\cos x} = \frac{1-\cos x}{\sqrt{3} + \sqrt{2+\cos x}} \approx \frac{x^2/2}{2\sqrt{3}} = \frac{x^2}{4\sqrt{3}}$.આમ,લક્ષની કિંમત $\lim_{x 	o 0} \frac{x^2}{x^2 / (4\sqrt{3})} = 4\sqrt{3}$ મળે.

$\lim _{x \rightarrow 0} \frac{(\operatorname{cosec} x-\cot x)(e^x-e^{-x})}{\sqrt{3}-\sqrt{2+\cos x}} = $

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