यदि $x = \log_e \left( \cot \left( \frac{\pi}{4} + \theta \right) \right)$ है,तो $\lim_{\theta \rightarrow 0} \frac{\theta}{(\sinh x)(\cosh x)} = $

$\mathop {\lim }\limits_{x \to 0} \,\frac{{x\,\cot \,\left( {4x} \right)}}{{{{\sin }^2}\,x\,{{\cot }^2}\,\left( {2x} \right)}}$ का मान ज्ञात कीजिए।

$\mathop {\lim }\limits_{x \to 0} \frac{\sin(mx)}{\tan(nx)} = $

$\lim _{x \rightarrow 0} \frac{\cos ax - \cos bx}{x^{2}}$ का मान ज्ञात कीजिए।

$\lim _{x \rightarrow 0} \frac{x \tan 4x - 2x \tan 2x}{(1 - \cos 4x)^2} = $

$\mathop {\lim }\limits_{h \to 0} \frac{{2\left[ {\sqrt 3 \sin \left( {\frac{\pi }{6} + h} \right) - \cos \left( {\frac{\pi }{6} + h} \right)} \right]}}{{\sqrt 3 h(\sqrt 3 \cos h - \sin h)}} = $