$f_n(x):[0,1]\rightarrow \mathbb{R}$ 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.