Determine the convergence, both pointwise and uniform, on [0,1] for each of the following sequences:

1) $\displaystyle S_n(x)= n^2x^2(1-cos1/[nx]), x not= 0; S_n(0)=0$.

2) $\displaystyle S_n(x)= nx/(x+n)$.

3) $\displaystyle S_n(x)= (1-cosnx)/nx, x not= 0; S_n(0)= 0$.

4) $\displaystyle S_n(x)= nsin(x/n)$.

I'm really struglling with these uniformly convergence problems, any help would be appreciated