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## Homework Statement

Let [tex]\lim_{x\to c} f(x) = A; A > 0[/tex], and [tex]\lim_{x\to c} g(x) = B[/tex].

Prove that [tex]\lim_{x\to c} f(x)^{g(x)} = A^{B}[/tex].

## The Attempt at a Solution

I really don't know how to approach this. I've been looking at it for an hour now, and while it seems obvious, I just don't know how to prove it. I've tried reducing it to limits of sequences and setting up an delta-epsilon proof, but it doesn't seem to pan out. Any ideas?