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.