જો x = log_e left( cot left( frac{pi}{4} + th | vedclass

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(B) આપેલ છે $x = \log_e \left( \cot \left( \frac{\pi}{4} + 	heta ight) ight)$.આપણે જાણીએ છીએ કે $\sinh x = -	an(2	heta)$ અને $\cosh x = \sec(2\

Vedclass · Accepted Answer

$-\frac{1}{2}$

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(B) આપેલ છે $x = \log_e \left( \cot \left( \frac{\pi}{4} + 	heta ight) ight)$.આપણે જાણીએ છીએ કે $\sinh x = -	an(2	heta)$ અને $\cosh x = \sec(2	heta)$.તેથી $(\sinh x)(\cosh x) = -	an(2	heta) \sec(2	heta) = -\frac{\sin(2	heta)}{\cos^2(2	heta)}$.હવે,લક્ષ $\lim_{	heta ightarrow 0} \frac{	heta}{-\sin(2	heta)/\cos^2(2	heta)} = \lim_{	heta ightarrow 0} -\frac{	heta}{\sin(2	heta)} \cdot \cos^2(2	heta) = -\frac{1}{2} \cdot 1 = -\frac{1}{2}$.

જો $x = \log_e \left( \cot \left( \frac{\pi}{4} + \theta \right) \right)$ હોય,તો $\lim_{\theta \rightarrow 0} \frac{\theta}{(\sinh x)(\cosh x)} = $

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