$\mathop {\lim }\limits_{x \to 0} x \log (\sin x) = $

$\lim _{x \rightarrow 1}\left((1-x) \tan \left(\frac{\pi x}{2}\right)\right)=$

$\mathop {\lim }\limits_{n \to \infty } {\left[ {\frac{{\sin \left( n \right)}}{{{n^2}}} + \log \left( {\frac{{en + 1}}{{n + e}}} \right)} \right]^n}$ ની કિંમત શોધો.

જો $f^{\prime \prime}(0)=k, k \neq 0,$ હોય, તો $\lim _{x \rightarrow 0} \frac{2 f(x)-3 f(2 x)+f(4 x)}{x^{2}}$ ની કિંમત શું થાય?

$\lim _{x \rightarrow 0} \left[ \frac{1}{x} - \frac{1}{e^x - 1} \right] = $

$\mathop {\lim }\limits_{x \to 0} \frac{{{{\tan }^{ - 1}}x}}{x}$ ની કિંમત શું છે?