આપેલ લક્ષની કિંમત શોધો: $\mathop {\lim }\limits_{x \to -1} \frac{x^{10}+x^{5}+1}{x-1}$

$\mathop {\lim }\limits_{x \to 3} \left\{ {\frac{{x - 3}}{{\sqrt {x - 2} - \sqrt {4 - x} }}} \right\} = $

$\lim _{x \rightarrow 0} \frac{\sin x \sin ^{-1} x}{x^2}$ ની કિંમત શોધો.

$\mathop {\lim }\limits_{x \to \infty } \frac{{{{(x + 1)}^{10}} + {{(x + 2)}^{10}} + \dots + {{(x + 100)}^{10}}}}{{{x^{10}} + {{10}^{10}}}}$ ની કિંમત શોધો.

$\mathop {\lim }\limits_{x \to 0} \frac{{1 - \cos (1 - \cos x)}}{{x\tan x - {x^2}}}$ ની કિંમત શોધો.

જો $\Delta(x) = \begin{vmatrix} e^x & -1 \\ \sin x - 1 & 1 \end{vmatrix}$ હોય,તો $\lim_{x \rightarrow 0} \frac{\Delta(x)}{x} = $