# Math Help - More Real Analysis: Epsilon-Delta: Uniformly Continuous

1. ## More Real Analysis: Epsilon-Delta: Uniformly Continuous

Another question, sorry Final Friday, senior year, this class is horrible

Let f: D-->R be uniformly continuous on D and let cED. Prove using an
epsilon-delta argument cf is uniformly continuous on D.

R = Real Numbers

2. Originally Posted by Vitava61
Another question, sorry Final Friday, senior year, this class is horrible

Let f: D-->R be uniformly continuous on D and let cED. Prove using an
epsilon-delta argument cf is uniformly continuous on D.

R = Real Numbers
let $\epsilon > 0$
Since f is uniformly continuous there exisits a delta for every epsilon such that

$|x-y|< \delta$ $|f(x)-f(y)|<\frac{\epsilon}{|c|}$

Now for $|x-c|< \delta$

$|cf(x)-cf(y)|=|c||f(x)-f(y)|<|c|\cdot \frac{\epsilon}{|c|}=\epsilon$

QED