Continuous function with $\lim_{x \rightarrow + \infty}f(x)=0$ and $\lim_{x \rightarrow - \infty}f(x)=0$ is uniformly continuous
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Suppose that $f:\Bbb R\to \Bbb R$ is continuous and that $f(x)\to 0$ as $x\to \pm\infty.$Prove that $f$ is uniformly continuous.
55749
Compactly supported continuous function is uniformly continuous
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Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
143174
property of continuous function
125024
Is this function uniformly continuous?
12997
Is a Cauchy sequence - preserving (continuous) function is (uniformly) continuous?
84785
Is $f(x)=x+\frac{x}{x+1}$ uniformly continuous on $(0,\infty)$
6620
If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
133405
$\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?
108115
If $f: [0,1]\rightarrow \mathbb{R}$ is continuous function positive
54893
$ \lim\limits_{x \rightarrow \ + \infty}(\sqrt{x^2 + 2x} - \sqrt{x^2 - 7x})$
15579
Show that $f$ is uniformly continuous if limit exists
95921
Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$
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Proving $f(x)=1/x$ on $(0,1 )$ is not uniformly continuous
5881
$\sqrt x$ is uniformly continuous
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$\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
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How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?