Uniform convergence of functions 

Consider the sequence $\{f_n\}$ defined by $f_n(x) = \frac{nx}{ 1 + nx}$ , for $x ≥ 0$.

a) Find $f(x) = \lim _{n→∞ }f_n(x).$
b) Show that for $a > 0$, $\{f_n\}$ converges uniformly to $f$ on $[a,∞)$.
c) Show that $\{f_n\}$ does not converge uniformly to $f$ on $[0,∞).$

Answer

Answers can only be viewed under the following conditions:
  1. The questioner was satisfied with and accepted the answer, or
  2. The answer was evaluated as being 100% correct by the judge.
View the answer

1 Attachment

Erdos Erdos
4.7K
The answer is accepted.
Join Matchmaticians Affiliate Marketing Program to earn up to a 50% commission on every question that your affiliated users ask or answer.