Find two parameters so that a function is continuous at a given point Let  
$$
f(x) = 
\begin{cases} 
  3x      & x < 3 \\ 
  a       & x = 3 \\ 
  x^2 + b & x > 3
\end{cases}
$$
Find $a, b$ so that $f(x)$ is continuous at $x=3$, then prove that $f(x)$ is continuous at $x=3$.
Guys, any explanation is helpful. 

$f(x)$ is continuous at $x=3$ if and only if 
$\lim_{x\rightarrow3^{-}}f(x)=\lim_{x\rightarrow3^{+}}f(x)=f(3)$, i.e. 
$\lim_{x\rightarrow3^{-}}3x=\lim_{x\rightarrow3^{+}}x^{2}+b=a$, so $9=9+b=a$, it means that $a=9$ and $b=0$.
