query: Is $t\sin\left(\frac1t\right)$ uniformly continuous on $(0,1)$?
positive_passages.docid: 149827
positive_passages.text: show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
negative_passages.docid: 117419
negative_passages.text: Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?
negative_passages.docid: 77943
negative_passages.text: If $f$ is continuous, then there exists $x+\frac{1}{n}\in[0,1]$ and $f\left(x+\frac{1}{n}\right)=f(x)$
negative_passages.docid: 132013
negative_passages.text: How do I show that if $f : [0,1] \to [0,1]$ is continuous, then there is some $c$ such that $f(c) = c$?
negative_passages.docid: 125723
negative_passages.text: Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
negative_passages.docid: 88640
negative_passages.text: Is $\sqrt x$ continuous at $0$? Because it is not defined to the left of $0$
negative_passages.docid: 63237
negative_passages.text: Proving that $\lim_{n \rightarrow\infty} \int_{0}^{\frac{\pi}{2}} \sin(t^n) dt =0$
negative_passages.docid: 108115
negative_passages.text: If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
negative_passages.docid: 153271
negative_passages.text: Fourier transform is uniformly continuous
negative_passages.docid: 131060
negative_passages.text: Is $\sqrt{x}$ uniformly continuous in $\mathbb{R}^+$?
negative_passages.docid: 21301
negative_passages.text: If nonnegative $f: [0,1] \rightarrow \mathbb{R}$ has a continuous $f''$, then $\int_0^1 \Big| \frac{f''(x)}{f(x)} \Big| \,dx >4$
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: 38761
negative_passages.text: Is the $ L^{p}$$[0,1]$ norm continuous in p?
negative_passages.docid: 26291
negative_passages.text: Does $\frac{nx}{1+n \sin(x)}$ converge uniformly on $[a,\pi/2]$ for all $a \in (0,\pi/2]$?
negative_passages.docid: 9614
negative_passages.text: How does the existence of a limit imply that a function is uniformly continuous
negative_passages.docid: 44057
negative_passages.text: Pointwise but not uniform convergence of continuous functions on $[0,1]$
negative_passages.docid: 65362
negative_passages.text: Does $\sum{\frac{\sin{(nx)}}{n}}$ converge uniformly for all $x$ in $[0,2\pi]$