# 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.

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### Proving that the pointwise limit of a sequence of function is 0. [on hold]

$$f_{n}(x)=\frac{n^3 x^{3/2}}{ 1 + n^4 x^2}.$$ I know that the pointwise limit is zero but I do not know how to prove it, could anyone help me in this please?
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### Finding a direct function for $f_n = f_{n-1} + (x-a_{n-1})^2$ where $a_{n-1}$ is root of $f_{n-1}$ closest to $\alpha$ and $f_1 = x-a$.

Problem Suppose $f_1 = (x-a)$ and $f_n = f_{n-1} + (x-a_{n-1})^2$ where $a_{n-1}$ is a root of $f_{n-1}$ closest to $0$. Is there a function for $f_n$ that only depends on $x$? Examples As a first ...
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### How to find all accumulation points of a sequence

First of all, I had I apology for snipping the equation out from my worksheet instead of writing it down. I'm new here. sequence I need to find all accumulation points I tried to solve it by hand, ...
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### How to deduce the sup of a function sequence $f_n$ without computing the derivative?
I came across the following function sequence: $$f_n = e^{-nx}\sin(nx)$$ I'm asked if the following sequence converges uniformly on the set of positive real numbers $[0,\infty[$. I found 2 ...