This is NOT L'Hopital's rule! You have taken the limit of the derivative of f which is NOT, in general, the limit of f.

(And even for that you would NOT get "0"- you would get which does not exist. Your f' does not have a limit.)

L'Hopital's rule says that if, at x= a, is the indeterminant form " " then provided the limits on the right exist.

That is, you differentiate the numerator and denominatorseparatelyNOT using the "quotient law".

Here, the numerator is and the denominator is which are 0 when x= 0, giving the form so we can apply L'Hopital's rule.

The derivative of is and the derivative of is . Those are both 0 at x= 0 so apply L'Hopital's ruleagain.

The derivative of is and the derivative of is which are 1 and 6 at x= 0.

The limit is .

Okay, here you2) Use L'Hopital's rule to obtain:

diddifferentiate numerator and denominator separately- although it should not be labeled "f' ".

It doesn't equal anything- is not a number, just shorthand for "gets larger without bound."The only problem i am having is what does equal to?

P.S

Here you have a fixed number, 1, over a denominator that gets larger and larger without bound- think of , , , etc. What is happening to those numbers as the denominator gets larger and larger?