Give an example, if possible, of a sequence { } 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 { } such that:
c.) is continuous and not differentiable but the sequence converges pointwise to a differentiable function
d.) {| |} converges pointwise but { } does not
That was all the problem said, so I take it that it should be nowhere differentiable. The only thing I can think of that is nowhere differentiable is:
g(x) = |x| on [-1,1]
h(x) = g(x) if x [-1,1];
otherwise, h(x-2) if x > 0 or h(x+2) if x < 0
f(x) = h( ) with n going from 0 to