query: Proof Verification: $x\sin(1/x)$ is continuous on $(0,1)$
positive_passages.docid: 150235
positive_passages.text: $\epsilon$-$\delta$ proof that $f(x) = x \sin(1/x)$, $x \ne 0$, is continuous
negative_passages.docid: 23617
negative_passages.text: Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
negative_passages.docid: 101701
negative_passages.text: Prove that $\ln x$ is not uniformly continuous on $(0,1]$
negative_passages.docid: 23288
negative_passages.text: Prove that $x^2<\sin x \tan x$ as $x \to 0$
negative_passages.docid: 72044
negative_passages.text: prove $x \mapsto x^2$ is continuous
negative_passages.docid: 94244
negative_passages.text: $\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
negative_passages.docid: 113086
negative_passages.text: Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
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: 38885
negative_passages.text: Prove the function is continuous, exercise from Conway's "Functions of One Complex Variable I"
negative_passages.docid: 62947
negative_passages.text: If $f(x)$ is equal to $x$ or $1-x$ when $x$ is rational/irrational, then $f$ is continuous only at $x=1/2$
negative_passages.docid: 127449
negative_passages.text: Uniform continuous of $f(x,y) = \sin(x^2+y)$
negative_passages.docid: 33628
negative_passages.text: Prove that $\sin(\sqrt x)$ not periodic
negative_passages.docid: 55839
negative_passages.text: Interior of the Graph of $\sin(1/x)$
negative_passages.docid: 154080
negative_passages.text: circular reasoning in proving $\frac{\sin x}x\to1,x\to0$
negative_passages.docid: 129856
negative_passages.text: Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
negative_passages.docid: 1986
negative_passages.text: Show $1/(1+ x^2)$ is uniformly continuous on $\Bbb R$.
negative_passages.docid: 61782
negative_passages.text: How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?