$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ is equal to

$\mathop {Lim}\limits_{n \to \infty } \frac{{{1^2}n + {2^2}(n - 1) + {3^2}(n - 2) + \dots + {n^2} \cdot 1}}{{{1^3} + {2^3} + {3^3} + \dots + {n^3}}}$ is equal to :

$\lim _{x \rightarrow 0} \frac{\sqrt{1+x^2}-\sqrt{1-x+x^2}}{3^x-1}$ is equal to

The value of $\lim _{x}$ ${\rightarrow 0} 2\left(\frac{1-\cos x \sqrt{\cos 2 x} \sqrt[3]{\cos 3 x} \ldots \sqrt[10]{\cos 10 x}}{x^2}\right)$ is ............

$\lim _{x \rightarrow 0} \frac{9^x-4^x}{x(9^x+4^x)} = $

$\lim _{x \rightarrow 0}(1+3x)^{\frac{2}{x}} = $