$\mathop {\lim }\limits_{x \to 0} \frac{{x\cos x - \sin x}}{{{x^2}\sin x}} = $

જો $\mathop {\lim }\limits_{x \to 0} \frac{{\log (3 + x) - \log (3 - x)}}{x} = k$ હોય,તો $k$ ની કિંમત શોધો.

ધારો કે $f(x) = \lim_{n \rightarrow \infty} \sum_{r=0}^n \left( \frac{2\tan(x/2^{r+1})}{1 - \tan^2(x/2^{r+1})} \right)$. તો $\lim_{x \rightarrow 0} \frac{e^x - e^{f(x)}}{x - f(x)}$ ની કિંમત . . . . . . . છે.

લક્ષની કિંમત શોધો: $\lim _{x \rightarrow \pi / 6} \frac{3 \sin x-\sqrt{3} \cos x}{6 x-\pi}$

$\lim _{x \rightarrow 1} (\log _3 3x)^{\log _x 8} = \ldots$

$\mathop {\lim }\limits_{x \to 0} \frac{{{2^x} - 1}}{{{{(1 + x)}^{1/2}} - 1}} = $