mathop {lim }limits_{x to 1} frac{{{x^2} - 1} | vedclass

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Question

(C) माना व्यंजक $L = \mathop {\lim }\limits_{x 	o 1} \frac{{{x^2} - 1}}{{{{\sin }^2}x + \cos x \cos (x + 2) - {{\cos }^2}(x + 1)}}$ है।सर्वसमिका $\co

Vedclass · Accepted Answer

$\frac{2}{\sin 2}$

Vedclass · Answer

(C) माना व्यंजक $L = \mathop {\lim }\limits_{x 	o 1} \frac{{{x^2} - 1}}{{{{\sin }^2}x + \cos x \cos (x + 2) - {{\cos }^2}(x + 1)}}$ है।सर्वसमिका $\cos A \cos B = \frac{1}{2} [\cos(A+B) + \cos(A-B)]$ का उपयोग करने पर,$\cos x \cos (x+2) = \frac{1}{2} [\cos(2x+2) + \cos 2]$ प्राप्त होता है।अतः,हर $\sin(x+1) \sin(x-1)$ में परिवर्तित हो जाता है।इस प्रकार,$L = \mathop {\lim }\limits_{x 	o 1} \frac{(x-1)(x+1)}{\sin(x+1) \sin(x-1)} = \frac{2}{\sin 2}$।

$\mathop {\lim }\limits_{x \to 1} \frac{{{x^2} - 1}}{{{{\sin }^2}x + \cos x \cos (x + 2) - {{\cos }^2}(x + 1)}}$ का मान है:

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