# Thread: A Question on Uniform Convergence

1. ## A Question on Uniform Convergence

Give an example of a uniformly convergent sequence $(f_{n})_{n\in\mathbb N}$ of continuously differentiable functions such that $(f\prime_{n})_{n\in\mathbb N}$ is not uniformly continuous.

Just preparing for my exams in a few weeks. Need to know the answer to this one to have as an example. Just in case!

2. Choose:

$f_n(x)=\dfrac{\sin nx}{n}$

Fernando Revilla

3. Many many thanks. Simple when you know how isn't it??

4. Originally Posted by garunas
Many many thanks. Simple when you know how isn't it??
No wonder. It is a typical counter example.

Fernando Revilla

5. Originally Posted by garunas
Give an example of a uniformly convergent sequence $(f_{n})_{n\in\mathbb N}$ of continuously differentiable functions such that $(f\prime_{n})_{n\in\mathbb N}$ is not uniformly continuous.
Sorry, what exactly is not uniformly continuous? Should $f'_n$ be not uniformly continuous for every $n$?

6. Originally Posted by emakarov
Sorry, what exactly is not uniformly continuous? Should $f'_n$ be not uniformly continuous for every $n$?
I supposed that is a typo and he meant " ... $(f'_n)$ not uniformly convergent".

Fernando Revilla

7. Yeah sorry I am a bit new to Latex