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# FInd lim. Apply 1'hopital's rule as many times as necessary, verifying your result after each application

lim e^2x/(x+5)^3

→∞

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- 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.

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