# Questions tagged [sequence-of-function]

Use this tag only when your query is about sequences of functions. Don't use this tag for any other sequence such as sequences of real numbers or sequences of complex numbers etc.

1,020 questions
Filter by
Sorted by
Tagged with
15 views

32 views

### Proving a sequence of functions isn't uniformly convergent

Let $f_n(x) = x^n(1-x^n)$. I need to prove that the sequence is not uniformly convergent in $[0,1]$. I have already proven that there is a pointwise convergence to $f(x)=0$. However, according to my ...
• 1,009
65 views

### Uniform convergence of $f_n(x) = \frac{\ln(1+\frac{x}{n})}{x+1}$ [duplicate]

Basically i have a problem proving the sequence in the title 1. Uniformly converges on a closed interval $[0,a]$ where $a > 0$ and 2. Uniformly converges on $[0,\infty).$ So far i have found the ...
60 views

• 454
29 views

• 387
67 views

### Find the rate of a sequence solving a polynomial inequality

Let $x\geq1$ be an integer and suppose that $n\to \infty$. Show that $x=O(n^c)$ if $$x^{1+a} \leq n + x^an^{-b}$$ for some $a>0$ and $b\geq1$. It looks to me that $x=O(n^{1/(1+a)})$, but I need to ...
• 215
1 vote
42 views

### Proving $f_n=nxe^{-nx}$ is not Uniformly convergent

To prove that $f_n= nxe^{-nx}$ is not uniformly convergent on $(0,\infty)$ I came up with a proof, But need to check whether that is correct or not... Proof: It is easy to see that $f_n$ converges ...
70 views

72 views

### Is it possible to construct a "divergent" sequence of functions?

I'm trying to understand pointwise versus uniform convergence of functions. So I want to find a sequence $\{f_n\}$ of functions $[0,1] \to \mathbb{R}$ that fails to converge pointwise to a function ...
89 views

• 7,613