Evaluate the limit using L'Hospital's rule

$\underset{x}{lim}10x{e}^{\frac{1}{x}}-10x$

Read the entry directions carefully!

The purpose of this question is to do the preliminary work to make a well$-$labeled sketch of the graph of the function

$f(x)=\frac{5x^2+5x+10}{x^2+x-56}$

First, find the critical values $($there should be three$)$:

Two of the critical values should be associated with asymptotes of this function. The remaining critical value should be a local maximum. What is the local maximum for this graph:

$x=$

$y=$

In addition to the vertical asymptotes, there is another asymptote.

Give the equation for this asymptote:

Hint: What is $\underset{x+-}{lim}f(x)?$

Finally, give the range for the function $f.$

$$

In your written work for this problem, please make a well$-$labled sketch of the function $y=f(x).$