If a function $f(x)=\left\{\begin{array}{cl}\frac{\tan (\alpha+1) x+\tan 2 x}{x} & \text { if } x>0 \\ \beta & \text { at } x=0 \text { is } \\ \frac{\sin 3 x-\tan 3 x}{x^3} & \text { if } x<0\end{array}\right.$

continuous at $x=0$, then $|\alpha|+|\beta|=$

$$ \lim \limits_{x \rightarrow 3} \frac{x^3-27}{x^2-9}= $$

If $f(x)=\left\{\begin{array}{ll}3 a x-2 b, & x>1 \\ a x+b+1, & x<1\end{array}\right.$ and

$\lim \limits_{x \rightarrow 1} f(x)$ exists, then the relation between $a$ and $b$ is

The function $f(x)=\left\{\begin{array}{ll}\frac{2}{5-x}, & x<3 \\ 5-x, & x \geq 3\end{array}\right.$ is