$\lim _{y \rightarrow 1}\left(\frac{1}{y^2-1}-\frac{2}{y^4-1}\right)=$

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

$\lim _{x \rightarrow \frac{\pi}{4}} \frac{2 \sqrt{2}-(\cos x+\sin x)^3}{1-\sin 2 x}=$

$\mathop {\lim }\limits_{x \to 0} f(x)$ और $\mathop {\lim }\limits_{x \to 1} f(x)$ ज्ञात कीजिए,जहाँ $f(x) = \begin{cases} 2x+3, & x \leq 0 \\ 3(x+1), & x > 0 \end{cases}$

यदि $\lim _{x \rightarrow 0} \frac{\cos 2x - \cos 4x}{1 - \cos 2x} = k$,तो $\lim _{x \rightarrow k} \frac{x^k - 27}{x^{k+1} - 81} = $

$\lim _{x \rightarrow 0} x^3 \left\{ \sqrt{x^2 + \sqrt{x^4 + 1}} - \sqrt{2} x \right\} = $