Give an example, if possible, of a sequence {$\displaystyle f_{n}$}$\displaystyle _{n \in N}$ of discontinuous functions on R which converges uniformly to:

a.) a discontinuous function on R

b.) a continuous function on R

Give an example of a sequence of functions {$\displaystyle f_{n}$}$\displaystyle _n \in N$ such that:

c.) $\displaystyle f_{n}$ is continuous and not differentiable but the sequence converges pointwise to a differentiable function

d.) {|$\displaystyle f_{n}$|}$\displaystyle _{n \in N}$ converges pointwise but {$\displaystyle f_{n}$}$\displaystyle _{n \in N}$ does not