Question

What if $\epsilon$ is infinity in the $\epsilon$-$\delta$ definition of limits?

score 843 · Answer 1 · 2020-06-18 08:14:13

843

Views

What if $\epsilon$ is infinity in the $\epsilon$-$\delta$ definition of limits?

Published on 18 Jun 2020 - 8:14

score 90 · Answer 2 · 2020-06-25 13:58:21

90

Views

Intuition behind being able to choose many different deltas when proving with epsilon delta limits

Published on 25 Jun 2020 - 13:58

score 231 · Answer 3 · 2020-06-25 16:38:28

231

Views

Epsilon-delta on a function with restricted range

Published on 25 Jun 2020 - 16:38

score 391 · Answer 4 · 2020-06-25 17:20:07

391

Views

Multiple possible delta in epsilon-delta

Published on 25 Jun 2020 - 17:20

score 182 · Answer 5 · 2020-06-28 02:16:59

182

Views

Proving limit by definition with absolute value

Published on 28 Jun 2020 - 2:16

score 109 · Answer 6 · 2020-06-28 07:01:16

109

Views

Prove that $g$ is also continuous at $x=0$.

Published on 28 Jun 2020 - 7:01

score 174 · Answer 7 · 2020-07-02 10:56:25

174

Views

An alternate definition of Limit

Published on 02 Jul 2020 - 10:56

score 94 · Answer 8 · 2020-07-03 16:35:14

94

Views

Defining rigorously, the intuition of Limits

Published on 03 Jul 2020 - 16:35

score 69 · Answer 9 · 2020-07-05 13:39:42

69

Views

About the proof using a simple epsilon delta.

Published on 05 Jul 2020 - 13:39

score 80 · Answer 10 · 2020-07-08 01:00:30

80

Views

Prove that $\sqrt{x} + x$ approaches $2$ as $x$ approaches $1$

Published on 08 Jul 2020 - 1:00

score 165 · Answer 11 · 2020-07-08 21:35:13

165

Views

Show that the sequence $x_{n+1} = \frac12(x_n+ \sqrt{x_n})$ converges and determine the limit.

Published on 08 Jul 2020 - 21:35

score 70 · Answer 12 · 2020-07-12 00:47:04

70

Views

Prove that $0<\lim\limits_{x\to \infty}f(x)<1\implies \lim\limits_{x\to \infty}\big(f(x)\big)^x=0$

Published on 12 Jul 2020 - 0:47

score 245 · Answer 13 · 2020-07-14 13:45:12

245

Views

Limits with epsilon-delta

Published on 14 Jul 2020 - 13:45

score 86 · Answer 14 · 2020-07-15 02:38:28

86

Views

in the $\epsilon$-$\delta$ definition of limit,would it be wrong if the $\epsilon$ is a rational number rather than a real number?

Published on 15 Jul 2020 - 2:38

score 100 · Answer 15 · 2020-07-20 22:08:42

100

Views

${f(x) = x^2 + x + 1}$ is continuous on ${\mathbb{R}}$

Published on 20 Jul 2020 - 22:08

List Question

What if $\epsilon$ is infinity in the $\epsilon$-$\delta$ definition of limits?

Intuition behind being able to choose many different deltas when proving with epsilon delta limits

Epsilon-delta on a function with restricted range

Multiple possible delta in epsilon-delta

Proving limit by definition with absolute value

Prove that $g$ is also continuous at $x=0$.

An alternate definition of Limit

Defining rigorously, the intuition of Limits

About the proof using a simple epsilon delta.

Prove that $\sqrt{x} + x$ approaches $2$ as $x$ approaches $1$

Show that the sequence $x_{n+1} = \frac12(x_n+ \sqrt{x_n})$ converges and determine the limit.

Prove that $0<\lim\limits_{x\to \infty}f(x)<1\implies \lim\limits_{x\to \infty}\big(f(x)\big)^x=0$

Limits with epsilon-delta

in the $\epsilon$-$\delta$ definition of limit,would it be wrong if the $\epsilon$ is a rational number rather than a real number?

${f(x) = x^2 + x + 1}$ is continuous on ${\mathbb{R}}$

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