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 be viewed only if
- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.
1 Attachment
The answer is accepted.
- answered
- 103 views
- $20.00
Related Questions
- Is it true almost all Lebesgue measurable functions are non-integrable?
- Find the extrema of $f(x,y)=x$ subject to the constraint $x^2+2y^2=2$
- [Real Analysis] Let $a>1$ and $K>0$. Show that there exists $n_0∈N$ such that $a^{n_0}>K$.
- A telephone line hanging between two poles.
- Calculus Integral Questins
- Two persons with the same number of acquaintance in a party
- How to parameterize an equation with 3 variables
- Prove that $S \subseteq X$ is nowhere dense iff $X-\overline{S}$ is dense.