Question

When is it appropriate and when is it not appropriate to use l'Hopital's Rule?

Answer 1

It is appropriate to use l'Hopital's rule when your fraction of two functions gives you either \[\infty/\infty \ or \ 0/0\] after substituting the value to which your variable is approaching. If you get any other indeterminate form, i.e. infinity - infinity, 0^0, etc, then you need to manipulate the expression until you get it into those two first indeterminate forms.

Answer 2

You don't always have to use l'Hopital's Rule right? If you can factor or otherwise find the limit without using l'Hopital's Rule you can do that too can't you? I'm trying to write an essay about this and it's not going well.

Answer 3

Of course, if you don't need to use l'Hopital's rule, then by all means go about your normal business! I'm not quite sure how you can write an entire essay about limit ratios of derivatives....