# Thread: Does f(0) exist?

1. ## Does f(0) exist?

Should it be 0? Since if x = 0 it is at 0? THANK YOU!!!

2. [quote=miss.strw;378426] Should it be 0? Since if x = 0 it is at 0? THANK YOU!!!

Evaluate the limit when x --> 0 of [f(x) - f(0)]/x , which is:

x^2*sin(1/x)/x = x*sin(1/x) --> 0 since sin(1/x) is bounded.

So f'(0) = 0

Tonio