# Continuity of arctan x / x at 0.

1. Oct 19, 2011

### mariush

1. The problem statement, all variables and given/known data
f:R->R is defined as f(x) when x$\neq 0$, and 1 when x=0.

Find f'(0).

2. Relevant equations

3. The attempt at a solution
Since I can prove that f is continuous at x=0, does that allow me to take the the limit of f'(x) as x-> 0, which is 0? It is quite easy to see that the correct answer must be f'(0)=0, but do i break any rules if I first differentiate f(x) and then look at the limit as x-> 0?

Thanks!

2. Oct 19, 2011

### SammyS

Staff Emeritus
Just use lim(h→0) (f(x+h)-f(x))/h