Question

How to prove that $\lim_{x\rightarrow0}\frac{1}{2x+1}=1$ using $\delta-\epsilon$ definition?

score 156 · Answer 1 · 2026-04-16 17:45:20

156

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How to prove that $\lim_{x\rightarrow0}\frac{1}{2x+1}=1$ using $\delta-\epsilon$ definition?

Published on 16 Apr 2026 - 17:45

score 716 · Answer 2 · 2026-04-10 15:10:35

716

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Proof diameter of a set equals diameter of its closure

Published on 10 Apr 2026 - 15:10

score 95 · Answer 3 · 2026-04-16 23:56:41

95

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If $q \neq 5$ or $k \neq 1$, do the following conditions follow?

Published on 16 Apr 2026 - 23:56

score 94 · Answer 4 · 2026-04-14 19:50:57

94

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Proving that any given element $hk$ appears $|H \cap K|$ times as a product in the list of $HK$

Published on 14 Apr 2026 - 19:50

score 359 · Answer 5 · 2026-04-10 02:43:23

359

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6 true or false questions in complex analysis

Published on 10 Apr 2026 - 2:43

score 44 · Answer 6 · 2026-04-14 04:35:02

44

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Proof verification of $x_n = \sum_{k=1}^n a_kq^k$ is Cauchy given $|a_k| \le C, |q| < 1, k\in\Bbb N$

Published on 14 Apr 2026 - 4:35

score 546 · Answer 7 · 2026-03-25 01:15:20

546

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Constant trajectory in Hamiltonian system

Published on 25 Mar 2026 - 1:15

score 326 · Answer 8 · 2026-04-17 04:33:14

326

Views

Prove that $\{x_n\}$ is a Cauchy sequence iff $\forall \epsilon > 0\ \exists N: \forall n > N \implies |x_n - x_N| < \epsilon$

Published on 17 Apr 2026 - 4:33

score 2k · Answer 9 · 2026-04-09 21:37:02

2k

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Application of Gronwall Inequality to existence of solutions

Published on 09 Apr 2026 - 21:37

score 331 · Answer 10 · 2026-04-17 02:58:17

331

Views

Showing that these vector fields commute on the image

Published on 17 Apr 2026 - 2:58

score 63 · Answer 11 · 2026-04-28 16:31:54

63

Views

If $f:A \to B$ is a bijection, show that $g:B \to A$ is a function.

Published on 28 Apr 2026 - 16:31

score 182 · Answer 12 · 2026-04-11 06:57:49

182

Views

Partial fraction failure for $\frac{1}{\sin(x-a)\sin(x-b)}$

Published on 11 Apr 2026 - 6:57

score 155 · Answer 13 · 2026-04-15 18:36:59

155

Views

Notation question related to $\mathbb{Q}(\sqrt{3})$.

Published on 15 Apr 2026 - 18:36

score 273 · Answer 14 · 2026-04-16 05:44:06

273

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Prove the inequality $\ln {(1+\frac{1}{x})}> \frac{2}{2x+1}$

Published on 16 Apr 2026 - 5:44

score 81 · Answer 15 · 2026-04-14 23:20:44

81

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Proof verification of $x_n = {1\over2^2}+{2\over3^2}+\cdots+{n\over(n+1)^2}$ diverges by the negation of Cauchy

Published on 14 Apr 2026 - 23:20

List Question

How to prove that $\lim_{x\rightarrow0}\frac{1}{2x+1}=1$ using $\delta-\epsilon$ definition?

Proof diameter of a set equals diameter of its closure

If $q \neq 5$ or $k \neq 1$, do the following conditions follow?

Proving that any given element $hk$ appears $|H \cap K|$ times as a product in the list of $HK$

6 true or false questions in complex analysis

Proof verification of $x_n = \sum_{k=1}^n a_kq^k$ is Cauchy given $|a_k| \le C, |q| < 1, k\in\Bbb N$

Constant trajectory in Hamiltonian system

Prove that $\{x_n\}$ is a Cauchy sequence iff $\forall \epsilon > 0\ \exists N: \forall n > N \implies |x_n - x_N| < \epsilon$

Application of Gronwall Inequality to existence of solutions

Showing that these vector fields commute on the image

If $f:A \to B$ is a bijection, show that $g:B \to A$ is a function.

Partial fraction failure for $\frac{1}{\sin(x-a)\sin(x-b)}$

Notation question related to $\mathbb{Q}(\sqrt{3})$.

Prove the inequality $\ln {(1+\frac{1}{x})}> \frac{2}{2x+1}$

Proof verification of $x_n = {1\over2^2}+{2\over3^2}+\cdots+{n\over(n+1)^2}$ diverges by the negation of Cauchy

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