query: $f:\mathbb{R}^{+}\to\mathbb{R}^{+}$ is uniformly continuous. Does $\lim_{x\to\infty}\frac{f(x+\frac{1}{x})}{f(x)}=1$ hold?
positive_passages.docid: 20658
positive_passages.text: Difficulty in finding a counterexample
negative_passages.docid: 26541
negative_passages.text: Is $\sum_{n=1}^{\infty}{\frac{\sin(nx)}n}$ continuous?
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: 153697
negative_passages.text: Is there a function $f: \mathbb{R} \to \mathbb{R}$ such that $\lim\limits_{x\to p}f(x)=\infty$ for every $p \in \mathbb{R}$
negative_passages.docid: 64169
negative_passages.text: Why isn't $\lim \limits_{x\to\infty}\left(1+\frac{1}{x}\right)^{x}$ equal to $1$?
negative_passages.docid: 155822
negative_passages.text: Does uniform convergence preserves absolute continuity?
negative_passages.docid: 91680
negative_passages.text: Does $\lim_{n\to \infty} \int^{\infty}_{-\infty} f_n(x) dx\, = \int^{\infty}_{-\infty} f(x)\,dx\,$?
negative_passages.docid: 20675
negative_passages.text: $L=\lim_{x\to\infty}(f(x)+f'(x))$ exists . Which of the following statements is\are correct?
negative_passages.docid: 119602
negative_passages.text: $f:\mathbb{R} \to \mathbb{R}$ be differentiable and $\lim\limits_{x\to\infty}f'(x)=1$, is $f(x)$ unbounded?
negative_passages.docid: 73812
negative_passages.text: Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
negative_passages.docid: 23617
negative_passages.text: Determine whether $f(x)={\sin x \over x}$ is uniformly continuous in $\mathbb R$
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: 96273
negative_passages.text: Is a continuous function $ f\colon(0,\infty)\to R$, such that $f(x)\leq f(nx)$ increasing?
negative_passages.docid: 111290
negative_passages.text: If $f$ continuous and $\lim_{x\to-\infty }f(x)=\lim_{x\to\infty }f(x)=+\infty $ then $f$ takes its minimum.
negative_passages.docid: 124779
negative_passages.text: Intuition for uniform continuity of a function on $\mathbb{R}$
negative_passages.docid: 125024
negative_passages.text: Is this function uniformly continuous?
negative_passages.docid: 117419
negative_passages.text: Why is $e^{x}$ not uniformly continuous on $\mathbb{R}$?