Showing uniform convergence (or lack of) on [0,1]

[dracond]

Homework Statement

Hello! I've been tasked with figuring out if the following is uniformly convergent on [0,1] and I could use push in the right direction:

sin(nx)

Homework Equations

The Attempt at a Solution

Would picking M=1 in the weierstrass-m test show it not uniformly convergent?

 

[quasar987]

Does it even converge pointwise?

 

[dracond]

Oops, it oscillates between [-1,1], no?
so does not converge pointwise.