If $f(x)=\left\{\begin{array}{l}\frac{\sqrt{1+x}-\sqrt{1-x}}{\sin x} \\ \boldsymbol{k}, x=0\end{array}, x \neq 0\right.$ is continuous at $x=0$, then $\boldsymbol{k}=$

$$ \mathop {\lim }\limits_{x \to 0} \frac{(1-\cos 2 x)(3+\cos x)}{x \tan 4 x} \text { is equal to: } $$

The value of $\mathop {\lim }\limits_{x \to 3}\left[\frac{1}{x-3}+\frac{9 x}{27-x^3}\right]$ is:

The function $y=||x|-1|$ is differentiable for all values of ' $x$ ' except