query: Prove that $f(x)=\sin x$ uniformly continuous on$(-\infty,\infty )$
positive_passages.docid: 102918
positive_passages.text: Prove $\sin x$ is uniformly continuous on $\mathbb R$
negative_passages.docid: 135449
negative_passages.text: Prove: $\frac1x$ is not a uniformly continuous function
negative_passages.docid: 95429
negative_passages.text: If $f$ is continuous with $ \int_0^{\infty}f(t)\,dt<\infty$ then which are correct?
negative_passages.docid: 129856
negative_passages.text: Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
negative_passages.docid: 84785
negative_passages.text: Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
negative_passages.docid: 57180
negative_passages.text: Techniques to prove a function is uniformly continuous
negative_passages.docid: 3856
negative_passages.text: Uniform Continuity of $x \sin x$
negative_passages.docid: 56567
negative_passages.text: Prove or disprove the uniform continuity of $f: \mathbb{C} \to \mathbb{C}, z \mapsto f(z)=\frac{z^2}{1+|z|}$
negative_passages.docid: 111470
negative_passages.text: Proof of differentiability of $f(x)$
negative_passages.docid: 47381
negative_passages.text: If $\lim_{x\to\infty} [f(x+1)-f(x)] =l$ then $\lim_{ x\to\infty}f(x)/x =l$ ($f$ is continuous)
negative_passages.docid: 150770
negative_passages.text: Why is $f^n(\xi(x))$ continuous over $x$?
negative_passages.docid: 5881
negative_passages.text: $\sqrt x$ is uniformly continuous
negative_passages.docid: 13747
negative_passages.text: Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
negative_passages.docid: 103124
negative_passages.text: Proving that $f(z)=\sum\limits_{n=1}^{\infty}\frac{z}{n(1+n|z|^{2})}$ converges uniformly on $\mathbb{C}$
negative_passages.docid: 74145
negative_passages.text: How to prove $x^{n}$ is not uniformly continuous
negative_passages.docid: 51247
negative_passages.text: $f$ be a continuous function maps Cauchy into Cauchy. Is $f$ uniformly continuous?
negative_passages.docid: 13257
negative_passages.text: How to prove this problem about uniform continuity