examine the sequence of functions defined by
f_n(x) = 2nx/n^p + x^2. for different values of p > 0.
a) show the function above converges to its limit function uniformly on the interval I = [0, infinity) iff p>2.
b)Show that when p > 4, M-Test be applied to show that g= SUM(f_n) converges uniformly on the interval I, but fails other p's.
c)Show that SUM(f_n) converges uniformly on any interval I =[0,a] whenever p > 2.