Find the horizontal and vertical asymptotes of the curve

Question

y=8x^x/e^x-9

x=

** I have figured out the two horizontal asymptotes. I could not figure out the vertical one.

Answer 1

There is no horizontal asymptotes because lim x→∞ 8x^x/(e^x - 9) = ∞.

To get vertical asymptote we set e^x - 9 = 0, e^x = 9, x = ln9 is vertical asymptote.