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:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
![Erdos](https://matchmaticians.com/storage/user/100028/thumb/matchmaticians-3empnt-file-5-avatar-512.jpg)
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.
- answered
- 516 views
- $20.00
Related Questions
- real analysis
- Compute $\lim_{n \rightarrow \infty} \ln \frac{n!}{n^n}$
- Evaluate the limit Please explain all steps
- Explain what the problem means in laymens terms.
- Improper integral
- Given $|f(x) - f(y)| \leq M|x-y|^2$ , prove that f is constant.
- Method of cylindrical shells
- Prove that $\int_0^1 \left| \frac{f''(x)}{f(x)} \right| dx \geq 4$, under the given conditions on $f(x)$