Prove Theorem.Theorem. [COMPARISON THEOREM FOR FUNCTIONS].Suppose that a ∈ R, that I is an...

Prove Theorem.

Theorem. [COMPARISON THEOREM FOR FUNCTIONS].

Suppose that a ∈ R, that I is an open interval which contains a, and that f,g are real functions defined everywhere on I except possibly at a. If f and g have limits as x approaches a and f (x) ≤ g(x) for all x ∈ I \{a}, then

We shall refer to this last result as taking the limit of an inequality.