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

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

The relationship between a and b for the continuous function

$f(x)=\left\{\begin{array}{ll}a x+1, & \text { if } x \leq 3 \\ b x+3, & \text { if } x>3\end{array}\right.$ at $x=3$ is