Question related to inequalities and limits that go to infinity

[eggmanneo]

I want to show that if $f(x) > g(x)$ $\forall x \in (-\infty, \infty)$ and $\displaystyle\lim_{x\to\infty}g(x)=\infty$, then $\displaystyle \lim_{x\to\infty}f(x)=\infty$. This result is true, correct? If so, what theorem should I use or reference to show this result? I wasn't sure if the squeeze theorem was application to this problem.

 

[JNeutron2186]

Have you considered the Squeeze Theorem?

 

[Bashyboy]

I may be entirely incorrect, but I don't think the squeeze theorem would be very helpful. f(x) isn't "squeezed" between two functions.

 

[jbunniii]

Consider what it means for $\lim_{x \rightarrow \infty} g(x) = \infty$ to be true. Given any $Y \in \mathbb{R}$, there is some $X \in \mathbb{R}$ such that $g(x) > Y$ for all $x > X$. Now apply the fact that $f(x) > g(x)$.