FInd lim. Apply 1'hopital's rule as many times as necessary, verifying your result after each application
- Anonymous1 decade agoFavorite Answer
This goes to ∞ / ∞, so we can apply l'Hopital's rule. Take the derivative of the top and bottom:
2e^(2x) / 3(x+5)^2
This too goes to ∞ / ∞, so apply l'Hopital's rule again.
4e^(2x) / 6(x+5) = 4e^(2x) / (6x+30)
This goes to ∞ / ∞, so apply l'Hopital's rule once again.
8e^(x) / (6)
This grows without bound, therefore the original expression has no limit.
It's important to keep checking at every step that the limit appears to go to ∞ / ∞ or 0/0, otherwise you can't apply the rule.