Limits

$\lim _{x \rightarrow \pi / 2} \frac{\left(1-\tan \left(\frac{x}{2}\right)\right)(1-\sin x)}{\left(1+\tan \left(\frac{x}{2}\right)\right)(\pi-2 x)^{3}}=?$

Given a real valued function ' $f$ ' such that $f(x)=\left\{\begin{array}{cc}\frac{\tan ^2\{x\}}{x^2-[x]^2} & \text { for } x\gt0 \\ 1 & \text { for } x=0 \\ \sqrt{\{x\} \cot \{x\}} & \text { for } x \lt…

Let $f(x)=\sin x, g(x)=\cos x, h(x)=x^2$ then $\lim _{x \rightarrow 1} \frac{f(g(h(x)))-f(g(h(1)))}{x-1}=$

If $f(x)=\left\{\begin{array}{l}x^2-1,0 < x < 2 \\ 2 x+3,2 \leq x < 3\end{array}\right.$, then the quadratic equation whose roots are $\lim _{x \rightarrow 2^{-}} f(x)$ and $\lim _{x \rightarrow 2^{+}} f(x)$ is

$\lim _{x \rightarrow 0} \frac{|\sin x|}{x}$ is equal to

The value of $\lim _{x \rightarrow 0} \frac{(1+x)^{\frac{1}{x}}-e+\frac{1}{2} e x}{x^2}$ is

The value of $\lim _{x \rightarrow 0} \frac{1-\cos (1-\cos x)}{x^4}$ is

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

$\lim _{x \rightarrow 0} \frac{2 \sin ^{2} 3 x}{x^{2}}$ is equal to

Value of $\lim _{x \rightarrow 0} \frac{a^{\sin x}-1}{\sin x}$ is

The value of $\text{lim} x→\frac{3π}{4}\frac{4{\sin}^{2}x\cosx-\cosx+\sinx}{\sinx+\cosx}$ is

The value of $a$, so that $\text{lim} x→0\frac{1}{{x}^{2}}({e}^{ax}-{e}^{x}-x)=\frac{3}{2}$, is