Let γn be a sequence of constants tending to [infinity]. Let fn(x) be the sequence of functions defined as follows:
fn (1/2) = 0, fn(x) = γn in the interval [1/2 - 1/n, 1/2), let fn(x)= γn in the interval (1/2. 1/2 + 1/n] and let fn(x) = 0 elsewhere. Show that: (a) fn(x) → 0 pointwise
(b) The convergence is not uniform. (c) fn(x) → 0 in the L^2 sense if γn = n^1/3
(d) fn(x) does not converge in the L^2 sense if γn = n.