**Problem:** Let f: R –> R be defined by . Then f is continuous but not uniformly continuous.

**Discussion:**

**True**

It is sufficient to show that there exists an such that for all there exist such that implies .

Assume . Let and .

Hence . (This is achieved by some simple algebra like rationalization )

Now if we take then but

Hence there exists an (= 0.99) such that for any value of we will get such that implies .

## Trackbacks/Pingbacks