Question

Prove Limit $5/(x+1)^3$ as $x \to -1^{-}$ is $-\infty$ epsilon delta proof

score 164 · Answer 1 · 2021-02-26 13:21:15

164

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Prove Limit $5/(x+1)^3$ as $x \to -1^{-}$ is $-\infty$ epsilon delta proof

Published on 26 Feb 2021 - 13:21

score 134 · Answer 2 · 2021-02-27 09:25:47

134

Views

Why cannot $\varepsilon$ be negative?

Published on 27 Feb 2021 - 9:25

score 61 · Answer 3 · 2021-02-28 22:01:26

61

Views

$f$ continuous and bounded on $\epsilon$ cover of $S$ implies $f$ continuous and bounded on $S$

Published on 28 Feb 2021 - 22:01

score 35 · Answer 4 · 2026-03-28 11:54:10

35

Views

if $p_L=\sum_{i=1}^{L}|a_i|\cdot \sum_{j=1}^{L} |b_j|$ is a Cauchy sequence then $\sum_{i\text{ or }j>L}|a_i|\cdot |b_j|<\varepsilon$

Published on 28 Mar 2026 - 11:54

score 60 · Answer 5 · 2026-03-30 10:13:26

60

Views

$\frac{1}{\cosh{x}}+\log\left ( \frac{\cosh{x}}{1+\cosh{x}} \right )$ for $x \rightarrow \pm \infty$ has a limit

Published on 30 Mar 2026 - 10:13

score 1.9k · Answer 6 · 2021-03-03 18:10:40

1.9k

Views

Use the definition of convergence to prove that the sequence $\left\{\frac{2n}{3n+2}\right\}$ converges.

Published on 03 Mar 2021 - 18:10

score 196 · Answer 7 · 2021-03-04 11:55:20

196

Views

If $\lim_{x\to \infty} f(x) = c\neq 0$ and $\lim_{x\to \infty} g(x) = 0$, then $\lim_{x\to \infty} \frac{f(x)}{g(x)}$ does not exist.

Published on 04 Mar 2021 - 11:55

score 116 · Answer 8 · 2026-04-04 17:43:47

116

Views

Uniform continuity general case

Published on 04 Apr 2026 - 17:43

score 135 · Answer 9 · 2021-03-05 16:44:58

135

Views

Use the $\epsilon$-$\delta$ definition of a limit to prove $\lim_{x\rightarrow 3} \frac{x+6}{x^{4}-4x^{3}+x^{2}+x+6}=-1$

Published on 05 Mar 2021 - 16:44

score 71 · Answer 10 · 2021-03-08 12:56:53

71

Views

Continuity Question, proving epsilon-delta

Published on 08 Mar 2021 - 12:56

score 89 · Answer 11 · 2021-03-09 16:03:51

89

Views

show function does not converge as h tends to 0

Published on 09 Mar 2021 - 16:03

score 70 · Answer 12 · 2021-03-09 23:32:33

70

Views

Proving that $f$ is continuous at $3$

Published on 09 Mar 2021 - 23:32

score 406 · Answer 13 · 2021-03-10 12:06:19

406

Views

proving 2 limits are equal

Published on 10 Mar 2021 - 12:06

score 38 · Answer 14 · 2021-03-10 15:35:23

38

Views

The graph of $f(x)$ lies below this line for small values of $x$

Published on 10 Mar 2021 - 15:35

score 64 · Answer 15 · 2021-03-10 16:05:14

64

Views

Question about a worked out problem regarding epsilon-delta Proof

Published on 10 Mar 2021 - 16:05

List Question

Prove Limit $5/(x+1)^3$ as $x \to -1^{-}$ is $-\infty$ epsilon delta proof

Why cannot $\varepsilon$ be negative?

$f$ continuous and bounded on $\epsilon$ cover of $S$ implies $f$ continuous and bounded on $S$

if $p_L=\sum_{i=1}^{L}|a_i|\cdot \sum_{j=1}^{L} |b_j|$ is a Cauchy sequence then $\sum_{i\text{ or }j>L}|a_i|\cdot |b_j|<\varepsilon$

$\frac{1}{\cosh{x}}+\log\left ( \frac{\cosh{x}}{1+\cosh{x}} \right )$ for $x \rightarrow \pm \infty$ has a limit

Use the definition of convergence to prove that the sequence $\left\{\frac{2n}{3n+2}\right\}$ converges.

If $\lim_{x\to \infty} f(x) = c\neq 0$ and $\lim_{x\to \infty} g(x) = 0$, then $\lim_{x\to \infty} \frac{f(x)}{g(x)}$ does not exist.

Uniform continuity general case

Use the $\epsilon$-$\delta$ definition of a limit to prove $\lim_{x\rightarrow 3} \frac{x+6}{x^{4}-4x^{3}+x^{2}+x+6}=-1$

Continuity Question, proving epsilon-delta

show function does not converge as h tends to 0

Proving that $f$ is continuous at $3$

proving 2 limits are equal

The graph of $f(x)$ lies below this line for small values of $x$

Question about a worked out problem regarding epsilon-delta Proof

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