# Convergence of a Sequence of functions Uniformly Mean Pointwise [duplicate]

For each of the following, give an example of a sequence of functions $f_n(x)$ that converges to f

A. uniformly but not in the mean square sense.

B. in the mean square sense but pointwise nowhere.

I know that for part A the domain of the function cannot be bounded. Please don't just repeat the definition of what it means to converge uniformly, in the mean square sense or pointwise. I'm looking for clues on how to choose a $f_n(x)$ that matches the conditions