Consider the function

$f(x)=\{\begin{array}{ccc}\frac{x^2+1x-30}{x-5}& if& x5\\ a& if& x=5\end{array}$

We want to define a such that the function $f$ is continuous for all $x.$

a$)$ The definition of the function $f$ for $x5$ can be simplified. After simplication, we have

$f(x)=$ for $x5$

b$)$ Compute the following limit$.$

$\underset{x5}{lim}f(x)=$

$$

c$)$ For which value of $a$ do we have that $f$ is continuous for all $x?$

Answer: $a=$