Analyze the following limits and find the vertical asymptotes of $f(x)=\frac{x-17}{x^2-289}$

a$.\underset{x17}{lim}f(x)$

b$.\underset{x-{17}^{-}}{lim}f(x)$

c$.\underset{x-{17}^{+}}{lim}f(x)$

a$.$ Rewrite the given limit in a way that can be evaluated using direct substitution.

$\underset{x17}{lim}\frac{x-17}{x^2-289}=\underset{x17}{lim}(\frac{1}{x+17})($Simplify your answer$)$

Now, evaluate the limit$.$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A$.\underset{x17}{lim}f(x)=($Simplify your answer.$)$

B$.$ The limit does not exist and is neither $$ nor $-.$