Given a piecewise, prove that it is continous and differentiable

[NWeid1]

Homework Statement

For f(x)= { sin(x)/x if x≠0 , 1 if x=0. (a) Show that f is continuous and differentiable for all x. (b) Show the derivative f'(x) is continous.

Homework Equations

The Attempt at a Solution

I know that if f is differentiable it is continous, so I need to focus on x=0 to show that the function is differentiable. And now I'm stuck lol

 

[HallsofIvy]

Well, what have you done? What does the "difference quotient" at x= 0?