query: Uniform continuity of $x \sin{\frac{1}{x}}$
positive_passages.docid: 26373
positive_passages.text: Uniform continuity of $f(x) = x \sin{\frac{1}{x}}$ for $x \neq 0$ and $f(0) = 0.$
negative_passages.docid: 106060
negative_passages.text: If $f$ is continuous and with a limit at infinity then $f$ is uniformly continuous
negative_passages.docid: 131866
negative_passages.text: Determine whether the function $f(x) = e^x \cos (1/x)$ is uniformly continuous on $A = (0,1)$.
negative_passages.docid: 17223
negative_passages.text: Continuity of an inverse function.
negative_passages.docid: 124779
negative_passages.text: Intuition for uniform continuity of a function on $\mathbb{R}$
negative_passages.docid: 71487
negative_passages.text: Real Analysis: Continuity of a Composition Function
negative_passages.docid: 153271
negative_passages.text: Fourier transform is uniformly continuous
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: 55749
negative_passages.text: Compactly supported continuous function is uniformly continuous
negative_passages.docid: 125088
negative_passages.text: show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
negative_passages.docid: 127449
negative_passages.text: Uniform continuous of $f(x,y) = \sin(x^2+y)$
negative_passages.docid: 94244
negative_passages.text: $\sin \frac{1}{x}$ is not uniformly continuous on $[1, \infty]$
negative_passages.docid: 3518
negative_passages.text: Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
negative_passages.docid: 131060
negative_passages.text: Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
negative_passages.docid: 36227
negative_passages.text: Show continuity or uniform continuity of $\phi: (C([0,1];\Bbb R ),||\cdot||_\infty )\to (\Bbb R, |\cdot | )$
negative_passages.docid: 141423
negative_passages.text: The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$
negative_passages.docid: 102918
negative_passages.text: Prove $\sin x$ is uniformly continuous on $\mathbb R$