# Thread: [SOLVED] limit as x approaches infinity w/ e

1. ## [SOLVED] limit as x approaches infinity w/ e

I am not getting anywhere I have this:
limit as x approaches infinity of (8+18e^3x)/(25e^5x+4) I keep applying L'Hopital's Rule but I just keep getting infinity over infinity.

2. Originally Posted by Amberosia32
I am not getting anywhere I have this:
limit as x approaches infinity of (8+18e^3x)/(25e^5x+4) I keep applying L'Hopital's Rule but I just keep getting infinity over infinity.
Applying L'Hospital's Rule is fine...

$\displaystyle \lim_{x \to \infty}\frac{8 + 18e^{3x}}{25e^{5x} + 4}$

$\displaystyle = \lim_{x \to \infty}\frac{54e^{3x}}{125e^{5x}}$ by L'Hospital

$\displaystyle = \lim_{x \to \infty}\frac{54}{125e^{2x}}$ by cancelling

What happens as the denominator gets infinitely large?

3. Originally Posted by Prove It
Applying L'Hospital's Rule is fine...

$\displaystyle \lim_{x \to \infty}\frac{8 + 18e^{3x}}{25e^{5x} + 4}$

$\displaystyle = \lim_{x \to \infty}\frac{54e^{3x}}{125e^{5x}}$ by L'Hospital

$\displaystyle = \lim_{x \to \infty}\frac{54}{125e^{2x}}$ by cancelling

What happens as the denominator gets infinitely large?
I didn't even think of canceling. Wow I feel really dumb, thanks so much.