Thread: L'Hopital's Rule

I need to apply L'hopital's rule as x approaches infinity for the following:

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

which gives me:

(2e^2x)/((x+5)^3) - (3e^2x)/((x+5)^4)

and a second time gives me:

(4e^2x)/((x+5)^3) - (12e^2x)/((X+5)^4) + (12e^2x)/((X+5)^5)


I guess my question is, how do I know when to stop (i.e. when have I found the limit as x approaches infinity with L'Hopital's rule?)

Apply L'hôpital's Rule until you get something except the indeterminate form. You should also stop when you get or too.

Hello, pennydooodle!

You don't seem to have a grip on L'Hopital's Rule . . .

Apply L'Hopital's Rule: .

You seem to be using some kind of strange Quotient Rule here . . .


Differentiate the numerator: .

Differentiate the denominator: .

. . Then: .


Apply L'Hopital again.



. . Then: .


Apply L'Hopital again:



. . Then: .

Thank you Soroban!

Now I see what I was doing wrong. I was attempting to differentiate the entire equation rather than each part on its own.

Thank you again!