Question

Show that the $\lim_{x\to 0} f(x)$ does not exist by $\varepsilon - \delta$ definition.

score 68 · Answer 1 · 2023-12-15 21:19:17

68

Views

Show that the $\lim_{x\to 0} f(x)$ does not exist by $\varepsilon - \delta$ definition.

Published on 15 Dec 2023 - 21:19

score 59 · Answer 2 · 2023-12-18 20:33:44

59

Views

Show that $\lim_{x\to a} = L \iff \lim_{x\to a^+} = L = \lim_{x\to a^-}$ by $\varepsilon - \delta$ definition

Published on 18 Dec 2023 - 20:33

score 137 · Answer 3 · 2023-12-19 14:58:37

137

Views

Prove $\,\lim\limits_{n\to\infty} \sqrt{\frac{4n+1}{n}}=2$

Published on 19 Dec 2023 - 14:58

score 132 · Answer 4 · 2026-03-28 11:32:13

132

Views

Is it true that if $a_n \to a$ and $\sum b_n \to b$ then $\sum a_n b_n \to ab$

Published on 28 Mar 2026 - 11:32

score 73 · Answer 5 · 2023-12-21 23:00:06

73

Views

Bounding $|g(x)|$ to prove product rule for limits

Published on 21 Dec 2023 - 23:00

score 112 · Answer 6 · 2023-12-29 02:58:06

112

Views

Proving $f(x) = \frac{1}{x}$ is not uniformly continuous on (0,1]

Published on 29 Dec 2023 - 2:58

score 74 · Answer 7 · 2024-01-01 07:04:42

74

Views

$\epsilon$ definition of a sequence not converging to a certain number

Published on 01 Jan 2024 - 7:04

score 86 · Answer 8 · 2026-03-28 22:24:19

86

Views

Gradient zero implies lipschitz with arbitrary constant

Published on 28 Mar 2026 - 22:24

score 107 · Answer 9 · 2024-01-04 10:51:10

107

Views

I have tried a proof $\;\lim\limits_{x\to0}x^2=1\,.\,$ I know it is wrong but could you tell me where?

Published on 04 Jan 2024 - 10:51

score 43 · Answer 10 · 2024-01-05 17:18:24

43

Views

Proving equality of $\lim_{x\to a} f(x)$ and $\lim_{h\to 0} f(a+h)$; is my proof valid?

Published on 05 Jan 2024 - 17:18

score 652 · Answer 11 · 2024-01-05 18:32:34

652

Views

Proving $a_n = \frac{(-1)^n n}{n+1}$ has no limit

Published on 05 Jan 2024 - 18:32

score 46 · Answer 12 · 2024-01-09 12:06:10

46

Views

Where am I wrong in epsilon-delta definition of continuity for $f(x, y) = x^2 / (x^2 + y^2)$?

Published on 09 Jan 2024 - 12:06

score 152 · Answer 13 · 2024-01-09 23:48:12

152

Views

"Epsilon Delta Definition of Limits"

Published on 09 Jan 2024 - 23:48

score 229 · Answer 14 · 2024-01-10 07:27:34

229

Views

Prove the limit using Epsion Delta Definition

Published on 10 Jan 2024 - 7:27

score 64 · Answer 15 · 2024-01-11 06:53:06

64

Views

prove $\lim_{x\to 0^-} \frac{x}{|x|} = -1$

Published on 11 Jan 2024 - 6:53

List Question

Show that the $\lim_{x\to 0} f(x)$ does not exist by $\varepsilon - \delta$ definition.

Show that $\lim_{x\to a} = L \iff \lim_{x\to a^+} = L = \lim_{x\to a^-}$ by $\varepsilon - \delta$ definition

Prove $\,\lim\limits_{n\to\infty} \sqrt{\frac{4n+1}{n}}=2$

Is it true that if $a_n \to a$ and $\sum b_n \to b$ then $\sum a_n b_n \to ab$

Bounding $|g(x)|$ to prove product rule for limits

Proving $f(x) = \frac{1}{x}$ is not uniformly continuous on (0,1]

$\epsilon$ definition of a sequence not converging to a certain number

Gradient zero implies lipschitz with arbitrary constant

I have tried a proof $\;\lim\limits_{x\to0}x^2=1\,.\,$ I know it is wrong but could you tell me where?

Proving equality of $\lim_{x\to a} f(x)$ and $\lim_{h\to 0} f(a+h)$; is my proof valid?

Proving $a_n = \frac{(-1)^n n}{n+1}$ has no limit

Where am I wrong in epsilon-delta definition of continuity for $f(x, y) = x^2 / (x^2 + y^2)$?

"Epsilon Delta Definition of Limits"

Prove the limit using Epsion Delta Definition

prove $\lim_{x\to 0^-} \frac{x}{|x|} = -1$

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