Can δ-ε Definitions Prove This Infinite Limit Scenario?

[Jimbo57]

Homework Statement

Prove, using the formal definition of limits:

If lim (x->inf) g(x) = inf and g(x) leq f(x) for x->a, then lim (x->a) f(x)=inf.

leq = less than or equal to.

Homework Equations

The Attempt at a Solution

Honestly, I'm not even sure where to start on this one. Anyone bored enough to show how they would solve it?

 

[SammyS]

Start with the δ-ε definition of a limit.

Show some work so we can help you. That's a rule for this Forum.

BTW: Don't you mean lim _{(x → a)} g(x) = ∞ , NOT lim _{(x → ∞)} ?