Limit question (from complex analysis)

[synapsis]

Homework Statement

This seems to be just a simple limit problem and I feel like I should know it but I'm just not seeing it.

I have a continuous function f, and a fixed w

I want to show that the limit (as h goes to 0) of the absolute value of:

(1/h)*integral[ f(z)-f(w) ]dz = 0 (the integral is over a contour)

Homework Equations

I believe the key to the problem is that f is continuous.

The Attempt at a Solution

For any a>0 there exists a b>0 such that z within b of w implies f(z) within a of f(w).

The problem is it seems to me like the 1/h term is going to infinity while the integral term is going to 0, which is indeterminate so I don't know how to get that the limit goes to 0.

 

[synapsis]

Oh, I have an idea. The contour I'm integrating over is the line connecting w+h to w. So I believe I can use the ML Estimate to show the limit goes to 0...