# Thread: find these horizontal asymptotes without calculator

1. ## find these horizontal asymptotes without calculator

y = 9e^x/e^x-4

I know it is 0 and 9 when I do it in my calculator, but I didn't quite understand algebraically. My professor said the e^x will cancel out but then why doesn't the 4 on the bottom get factored in?

2. Originally Posted by BugzLooney
y = 9e^x/e^x-4

I know it is 0 and 9 when I do it in my calculator, but I didn't quite understand algebraically. My professor said the e^x will cancel out but then why doesn't the 4 on the bottom get factored in?
divide every term by $\displaystyle e^x$ ...

$\displaystyle y = \frac{9}{1 - \frac{4}{e^x}}$

as $\displaystyle x \to \infty$ , $\displaystyle \frac{4}{e^x} \to 0$ ... what's left?

3. Hey yea I think I had it before you posted but thank you. Wanted to make sure though just in case I couldn't.