Question

Limit problem: I have an answer, but could somebody please check it? Thanks!

Answer 1

It's a long problem, so please give me a minute to type.

Answer 2

Let f and g be functions that are differentiable for all real numbers.
g(x) doesn't equal 0 for x doesn't equal 0
if lim x->0 f(x)= lim x->0 g(x)= 0,
and lim x->0 f'(x)/g'(x) exists, what is lim x->0 f(x)/g(x) ?
I think it is 0, would I be correct?

Answer 3

This is a multiple choice question, if you want to see the possible choices...
anyway, thank you for coming to help!

Answer 4

i would say not
you don't know what the limit is
it could be 0 but it is undermined

Answer 5

the answer is
\[\lim_{x\to 0}\frac{f'(x)}{g'(x)}\] whatever that is
that is l'hopitals rule

Answer 6

oh, okay. That just so happens to be one of the answers. So the limit exists, but is undetermined, and using l'hopital's rule is the answer?

Answer 7

yes, if \[\lim_{x\to 0}\frac{f'(x)}{g'(x)}\] exists, that is the limit