Consider the following function.

$f(x)=\frac{9e^x}{e^x-6}$

Find the value$($s$)$ of $x$ such that $e^x-6=0.($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

$x=$

$$

Does there exist a real number $c$ such that $\underset{xc}{lim}\frac{9e^x}{e^x-6}$ is an indeterminate form?

Yes

$$ No

Find the following limits$.$

$\underset{x-}{lim}\frac{9e^x}{e^x-6}=$

$\underset{x}{lim}\frac{9e^{\frac{y}{x}}}{e^x-6}=$

Find the horizontal and vertical asymptotes of the curve. You may want to use a graphing calculator $($or computer$)$ to check your work by graphing the curve and estimating the asymptotes. $($Enter your answers as comma$-$separated lists. If an answer does not exist, enter DNE.$)$

$x=$

$$

$y=$

$$