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Question about limits at infinity: $f(x) < g(x)$ and $f(x) < \epsilon$ imply $g(x) < \epsilon$?

score 64 · Answer 1 · 2023-01-05 00:12:29

64

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Question about limits at infinity: $f(x) < g(x)$ and $f(x) < \epsilon$ imply $g(x) < \epsilon$?

Published on 05 Jan 2023 - 0:12

score 35 · Answer 2 · 2023-01-05 18:35:02

35

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Evaluate the limit when $\frac{x + y}{x^2 + 1}$ approaches $(0,0)$ using the epsilon delta definition

Published on 05 Jan 2023 - 18:35

score 326 · Answer 3 · 2026-04-06 12:59:21

326

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Proving $f(x) = x^2$ is not uniformly continuous on the real ine

Published on 06 Apr 2026 - 12:59

score 26 · Answer 4 · 2026-04-06 12:58:49

26

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proving that a function that's continous on $[a, +\infty$) with an horizontal or oblique asymptote (at +$\infty$) is uniformally continious

Published on 06 Apr 2026 - 12:58

score 115 · Answer 5 · 2023-01-13 20:08:09

Why is $1$ included in the definition of $\delta$ when proving the limit of $\frac{\sin(x)}{x}$ as $x$ approaches $0$ using epsilon-delta proof?

score 47 · Answer 6 · 2026-04-09 09:29:41

47

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Subtle differences in limit definitions

Published on 09 Apr 2026 - 9:29

score 233 · Answer 7 · 2023-01-15 18:18:00

233

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Does $\displaystyle \lim_{x \rightarrow 0} \frac{\sin\left(x \sin \left( \frac 1x \right) \right)}{x \sin \left( \frac 1x \right)}$ exist?

Published on 15 Jan 2023 - 18:18

score 57 · Answer 8 · 2026-04-05 05:24:33

57

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A stricter limit where $0<|x-a|<\delta \Rightarrow \color{red}{0<} |f(x) - L| < \varepsilon$?

Published on 05 Apr 2026 - 5:24

score 35 · Answer 9 · 2023-01-24 07:20:18

Show that $f(x_{0}\cdots x_{n}) = (\frac{x_{0}}{x_{i}}\cdots \frac{x_{i-1}}{x_{i}},\frac{x_{i+1}}{x_{i}},\cdots \frac{x_{n}}{x_{i}})$ is continuous.

score 650 · Answer 10 · 2026-03-27 14:58:55

650

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Prove $\beta$ = inf E iff for every $\epsilon>0$ there exists a $y \in E$ such that $y<\beta + \epsilon$

Published on 27 Mar 2026 - 14:58

score 133 · Answer 11 · 2023-01-26 02:14:48

133

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Continuity of function of two variable by Epsilon-Delta technique.

Published on 26 Jan 2023 - 2:14

score 108 · Answer 12 · 2023-01-27 16:44:21

108

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Prove that the set $B = \{x \in\mathbb R^n \mid\operatorname{dist}(x,A) > 0\}$ is open.

Published on 27 Jan 2023 - 16:44

List Question

Question about limits at infinity: $f(x) < g(x)$ and $f(x) < \epsilon$ imply $g(x) < \epsilon$?

Evaluate the limit when $\frac{x + y}{x^2 + 1}$ approaches $(0,0)$ using the epsilon delta definition

Proving $f(x) = x^2$ is not uniformly continuous on the real ine

proving that a function that's continous on $[a, +\infty$) with an horizontal or oblique asymptote (at +$\infty$) is uniformally continious

Why is $1$ included in the definition of $\delta$ when proving the limit of $\frac{\sin(x)}{x}$ as $x$ approaches $0$ using epsilon-delta proof?

Subtle differences in limit definitions

Does $\displaystyle \lim_{x \rightarrow 0} \frac{\sin\left(x \sin \left( \frac 1x \right) \right)}{x \sin \left( \frac 1x \right)}$ exist?

A stricter limit where $0<|x-a|<\delta \Rightarrow \color{red}{0<} |f(x) - L| < \varepsilon$?

Show that $f(x_{0}\cdots x_{n}) = (\frac{x_{0}}{x_{i}}\cdots \frac{x_{i-1}}{x_{i}},\frac{x_{i+1}}{x_{i}},\cdots \frac{x_{n}}{x_{i}})$ is continuous.

Prove $\beta$ = inf E iff for every $\epsilon>0$ there exists a $y \in E$ such that $y<\beta + \epsilon$

Continuity of function of two variable by Epsilon-Delta technique.

Prove that the set $B = \{x \in\mathbb R^n \mid\operatorname{dist}(x,A) > 0\}$ is open.

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