Show that $f$ is uni. cont. on $(a,b)$ if and only if it is continuous $(a,b)$ and $\lim\limits_{x\to a^+}f(x)$ and $\lim\limits_{x\to b^-}f(x)$ exist

score 280 · Answer 8 · 2026-03-26 01:12:43

280

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Show f is unif. cont. on $\Bbb{R}$ if it is cont. on $\Bbb{R}$ and $\lim\limits_{x\to +\infty}f(x)$ and $\lim\limits_{x\to -\infty}f(x)$ exist

Published on 26 Mar 2026 - 1:12

score 1.2k · Answer 9 · 2026-03-26 02:54:42

1.2k

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Is $x^2$ uniformly continuous on $\Bbb{R^+}?$

Published on 26 Mar 2026 - 2:54

score 1.3k · Answer 10 · 2018-05-10 18:34:14

1.3k

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Proof that $g(x) = xf(x)$ is differentiable at 0 given that f is continuous at 0

Published on 10 May 2018 - 18:34

score 156 · Answer 11 · 2018-05-10 18:39:47

156

Views

Is $x\sin(\frac{1}{x}),\;0<x<\infty$ uniformly continuous?

Published on 10 May 2018 - 18:39

score 144 · Answer 12 · 2026-03-26 01:10:56

144

Views

Prove that $\frac{1}{x-1}$ is not uniformly continuous on (0,1)

Published on 26 Mar 2026 - 1:10

score 39 · Answer 13 · 2018-05-10 22:11:31

39

Views

Showing that a function is continuous for $x$

Published on 10 May 2018 - 22:11

score 168 · Answer 14 · 2018-05-11 07:52:55

168

Views

Type of discontinuity.

Published on 11 May 2018 - 7:52

score 1k · Answer 15 · 2018-05-11 15:42:54

1k

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Differentiability of $h(x)=x^2\sin(1/x)$ for $x\in\mathbb{R} \backslash \{0\}$ and $h(0)=0$ and continuity of derivative

Published on 11 May 2018 - 15:42

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