You are Here: Home >< Maths

# Uniform continuity example. watch

1. Is f: (0,1) -> R defined by f(x) = (x^2)cos(1/x) uniformly continuous?

I don't know any proof methods for uniform continuity and wondered if someone could explain it to me.

Thanks.
2. (Original post by Ben77)
Is f: (0,1) -&gt; R defined by f(x) = (x^2)cos(1/x) uniformly continuous?

I don't know any proof methods for uniform continuity and wondered if someone could explain it to me.

Thanks.
Use the mean value theorem http://en.wikipedia.org/wiki/Mean_value_theorem By differentiating, you can get upper/lower bounds on f'(c), and hence get an upper bound on |(f(b)-f(a))/(b-a)| which will work for any a and b.

You can then use this for an epsilon-delta proof, where you show that if |b-a| is sufficiently small then |f(b)-f(a)| is less than epsilon.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: November 30, 2011
Today on TSR

### Uni league tables

Do they actually matter?

### University open days

• University of Exeter
Wed, 24 Oct '18
Wed, 24 Oct '18
• Northumbria University
Wed, 24 Oct '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams