If $\lim\limits_{x \rightarrow 1} \frac{x^4-1}{x-1}=\lim\limits_{x \rightarrow k} \frac{x^3-k^3}{x^2-k^2}$, then the value of K is :

Evaluate: $\lim _\limits{x \rightarrow 0} \frac{\sqrt[3]{1+x}-\sqrt[3]{1-x}}{x}$

The function $f(x)=\left\{\begin{array}{l}\frac{|x|}{x}, \text { if } x \neq 0 \\ 0, \text { if } x=0\end{array}\right.$ is discontinuous at

$\lim _\limits{\theta \rightarrow \frac{\pi}{2}} \frac{1-\sin \theta}{\left(\frac{\pi}{2}-\theta\right) \cos \theta}$ is equal to :