- #1

Degeneration

- 23

- 0

## Homework Statement

a in R is finite, f,g are differentiable on R

[tex]\lim_{\substack{x\rightarrow a}} f(x)=\infty[/tex]

[tex]\lim_{\substack{x\rightarrow a}} g(x)=\infty[/tex]

[tex]g(x), g'(x)[/tex] not equal to zero

[tex]\lim_{\substack{x\rightarrow a}} f'(x)/g'(x)=\infty[/tex]

Show [tex]\lim_{\substack{x\rightarrow a}} f(x)/g(x)=\infty[/tex]

## Homework Equations

I'm sure you need to use the MVT

f'(c)/g'(c) = (f(x) - f(a))/(g(x) - g(a))

## The Attempt at a Solution

I'm starting out trying to use the continuity definition, but it seems to be going nowhere with a infinite limit.

For every number [tex]N[/tex] there is a [tex]\delta > 0[/tex] s.t. [tex]f'(x)/g'(x) > N[/tex] when [tex]0 < |x - a| < \delta[/tex]

Additionally, I can't just say lim x->a f'(x)/g'(x) = infinity = L and then use epsilon delta, since I don't know if it works for extended reals. Where can I go from here?