query: Show that $f_n(x)=n^2x^n(1−x)$ converges pointwise to $0$ using epsilon argument from definition
positive_passages.docid: 148410
positive_passages.text: How do I show $f_n(x)=n^2 x^n(1-x)$ pointwise converges to $0$ on $[0,1]$?
negative_passages.docid: 140901
negative_passages.text: Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$
negative_passages.docid: 136594
negative_passages.text: Proving the existence of a sequence of polynomials convergent to a continuous function $f$.
negative_passages.docid: 20359
negative_passages.text: Proof of radius of convergence exponential function
negative_passages.docid: 125925
negative_passages.text: Convergence of $f_n(x)=x^n(1-x)^n$
negative_passages.docid: 65474
negative_passages.text: Given sequence of $L-$Lipschitz functions which converges pointwise, prove uniform convergence
negative_passages.docid: 41482
negative_passages.text: $f_n → f$ uniformly on $S$ and each $f_n$ is cont on $S$. Let $(x_n)$ be a sequence of points in $S$ converging to $x \in S$. Then $f_n(x_n) → f(x)$.
negative_passages.docid: 44647
negative_passages.text: Does pointwise convergence of continuous functions on a compact set to a continuous limit imply uniform convergence on that set?
negative_passages.docid: 138317
negative_passages.text: weak convergence in $l^p$ implies bounded and pointwise convergence
negative_passages.docid: 5229
negative_passages.text: Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.
negative_passages.docid: 142645
negative_passages.text: $f_n$ converges uniformly on $[a,b]$ to some function $f$
negative_passages.docid: 42817
negative_passages.text: proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
negative_passages.docid: 133707
negative_passages.text: Notions of strong and weak convergence for $L^{2}(\mathbb R, \lambda)$ where $f_{n}(x)=1_{[n,n+1]}(x)$
negative_passages.docid: 115840
negative_passages.text: Showing equality of sequence of holomorphic functions to limit function if converges uniformly locally
negative_passages.docid: 52545
negative_passages.text: Prove limit converges in definition of $e.$
negative_passages.docid: 129087
negative_passages.text: Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
negative_passages.docid: 67453
negative_passages.text: If $x_{n}$ is decreasing and $\sum x_{n}$ converges, prove that $\lim nx_{n} = 0$