$f_n(x):[0,1]\rightarrow \mathbb{R}$ defined by $f_n(x)= \sin(n\pi x)$ if $x\in [0,1/n]$, and $f_n(x)=0$ if $x\in (1/n,1]$ Then
It does not converge pointwise.
It converges pointwise but the limit is not continous.
It converges pointwise but not uniformly.
It converges uniformly.