query: How to prove $f$ can be uniformly approximated on $[1,\infty )$ by a function $g$, using Weierstrass theorem.
positive_passages.docid: 155190
positive_passages.text: Stone-Weierstrass theorem with $p(1/x)$
negative_passages.docid: 13257
negative_passages.text: How to prove this problem about uniform continuity
negative_passages.docid: 77644
negative_passages.text: polynomial converges uniformily to analytic function
negative_passages.docid: 98282
negative_passages.text: Prove that the function $\xi\in R \mapsto {e^{i\cdot \xi\cdot λ}-1\over i\cdot \xi}-λ$ is $C^{\infty}$
negative_passages.docid: 118362
negative_passages.text: Determine whether $f_n(x)=\frac{x^n}{\sqrt{3n}}$ for $x \in [0,1]$ is uniformly convergent
negative_passages.docid: 15284
negative_passages.text: $f$ defined on $[1,\infty )$ is uniformly continuous. Then $\exists M>0$ s.t. $\frac{|f(x)|}{x}\le M$ for $x\ge 1$.
negative_passages.docid: 150896
negative_passages.text: Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
negative_passages.docid: 75735
negative_passages.text: Let $f$ be a continuous function on an interval around $0$ and let $a_i=f(\frac{1}{i})$ (for large enough $i$)
negative_passages.docid: 18153
negative_passages.text: To prove that $f_n(x) = \frac{nx}{1+n^2x^2}$ does not uniformly converge to $f(x) = 0$ on $[0,1]$
negative_passages.docid: 135700
negative_passages.text: Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
negative_passages.docid: 153300
negative_passages.text: Uniform approximation by even polynomial
negative_passages.docid: 149055
negative_passages.text: Uniform convergence of $\sum\limits_{k=1}^{\infty}\dfrac{kf(x^2)}{1+k^3f(x^2)^2}$
negative_passages.docid: 44458
negative_passages.text: Uniform limit of holomorphic functions
negative_passages.docid: 41037
negative_passages.text: Prove that $f'(a)=\lim_{n\to\infty}\frac{f(b_n)-f(a_n)}{b_n-a_n}$ under some conditions
negative_passages.docid: 156727
negative_passages.text: A step in the proof of Characterization of $W^{1,\infty}$
negative_passages.docid: 10408
negative_passages.text: Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
negative_passages.docid: 14067
negative_passages.text: If f uniformly continous then $|f(x)|\leq C\cdot (1+|x|)$ for constant C