A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists.
Show that each of the following functions has a horizontal asymptote by calculating the given limit.

Question

A function is said to have a horizontal asymptote if either the limit at infinity exists or the limit at negative infinity exists.
Show that each of the following functions has a horizontal asymptote by calculating the given limit.

anonymous · Answer

$$\lim_{x \rightarrow \infty} \frac{(\sqrt{x^{2}+5x})}{ 13-9x }$$

and...

$$\lim_{x \rightarrow -\infty} \frac{(\sqrt{x^{2}+5x})}{ 13-9x }$$