query: Uniform continuity of $\frac{\sin(x)}{x}$
positive_passages.docid: 23617
positive_passages.text: Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
negative_passages.docid: 37812
negative_passages.text: Prove that the function$\ f(x)=\sin(x^2)$ is not uniformly continuous on the domain $\mathbb{R}$.
negative_passages.docid: 31685
negative_passages.text: Differentiability of $f(x) = x^2 \sin{\frac{1}{x}}$ and $f'$
negative_passages.docid: 125910
negative_passages.text: Continuity of Integration for a measurable function
negative_passages.docid: 15727
negative_passages.text: show that if $f$ is uniformly differentiable then prove that $f'$ is continuous
negative_passages.docid: 131485
negative_passages.text: Continuity of $\frac{x^3y^2}{x^4+y^4}$ at $(0,0)$?
negative_passages.docid: 127538
negative_passages.text: Show $f(x)=x\ln x$ is not uniformly continuous
negative_passages.docid: 26541
negative_passages.text: Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?
negative_passages.docid: 84785
negative_passages.text: Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
negative_passages.docid: 46642
negative_passages.text: Continuity of $\sin(x)/x$
negative_passages.docid: 125745
negative_passages.text: continuity of power series
negative_passages.docid: 132946
negative_passages.text: Continuous and bounded imply uniform continuity?
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: 53627
negative_passages.text: Proving continuity of $f$
negative_passages.docid: 26373
negative_passages.text: Uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ for $x \neq 0$ and $f(0) = 0.$
negative_passages.docid: 13257
negative_passages.text: How to prove this problem about uniform continuity
negative_passages.docid: 125723
negative_passages.text: Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$