$(10pts.$

Consider the function

$f(x)=\{\begin{array}{ccc}\sqrt[\phantom{2}]{x^2+36}& if& x0\\ \frac{x^2+1}{x+1}& \text{i}\text{f}\text{s}\text{s}\text{o}\text{r}& 0=1\end{array}$

where $m$ is a constant.

$($a$)$ Using the conditions for continuity, determine if $f(x)$ is c tinuous at this point, indicate the type of discontinuity.

$\underset{x{0}^{-}}{lim}\sqrt[\phantom{2}]{0^2+36}=\sqrt[\phantom{2}]{36}=6(0)+$

$\underset{x{0}^{+}}{lim}\frac{x^2+1}{x+1}=\frac{(0{)}^2+1}{0+1}=\frac{1}{1}=1$

$5x+m$

$($b$)$ Using the conditions for continuity, find a value of $m$ for which $f(x)$ is continuous at $x=1.$

$\sqrt[\phantom{2}]{1^2+36}=\sqrt[\phantom{2}]{37}$