a. Show that lim( n goes to infinity) f_n(x)=0
Hint: Use the mean value theorem for f_n(x) on [0,x]
b. Show that f_n(x) converges uniformly to 0 on [0,a] for a fixed a in [0,infinity).
c. Is it true that f_n(x) converges uniformly to 0 on [0, infinity)? Justify your answer.© BrainMass Inc. brainmass.com March 21, 2019, 9:05 pm ad1c9bdddf
Then we have
(a) I claim that .
We fixed an . According to the Mean Value Theorem, we have
, where ...
Limits and uniform convergence are reiterated.