Question

Prove formula $\operatorname{arctanh} x = \frac12\,\ln \left(\frac{1+x}{1-x}\right)$

score 6.4k · Answer 1 · 2026-03-25 09:29:21

6.4k

Views

Prove formula $\operatorname{arctanh} x = \frac12\,\ln \left(\frac{1+x}{1-x}\right)$

Published on 25 Mar 2026 - 9:29

score 488 · Answer 2 · 2026-04-09 05:29:38

488

Views

Proof of an inequality using analytic geometry

Published on 09 Apr 2026 - 5:29

score 298 · Answer 3 · 2026-03-31 15:35:28

298

Views

On Stirling Number

Published on 31 Mar 2026 - 15:35

score 660 · Answer 4 · 2026-04-01 20:26:58

660

Views

How to obtain the quadratic equation when given that the sum of the roots at equal to 47 and the product of the roots is -59?

Published on 01 Apr 2026 - 20:26

score 3.1k · Answer 5 · 2026-03-25 19:06:51

3.1k

Views

For Fibonacci numbers: $\gcd(F_m, F_n) = F_{\gcd(m, n)}$

Published on 25 Mar 2026 - 19:06

score 103 · Answer 6 · 2026-03-28 02:21:02

103

Views

Combinations with Conditional Probability

Published on 28 Mar 2026 - 2:21

score 55 · Answer 7 · 2026-03-27 15:18:54

55

Views

Solution to system of first order wave PDEs

Published on 27 Mar 2026 - 15:18

score 66 · Answer 8 · 2026-03-29 10:15:23

66

Views

Prove that $ I + J = R \iff b + J $ is invertible in $ R / J$, where $ I = \langle b \rangle$

Published on 29 Mar 2026 - 10:15

score 618 · Answer 9 · 2026-04-01 22:41:32

618

Views

Is the substitution of variables allowed in proofs?

Published on 01 Apr 2026 - 22:41

score 379 · Answer 10 · 2026-03-29 19:28:27

379

Views

Differentiability of the function $f(x,y)=\begin{cases} \frac{xy}{x^2+y^2}, & \text{if $(x,y)\ne(0,0)$}\\ 0, & \text{otherwise} \end{cases}$

Published on 29 Mar 2026 - 19:28

score 34 · Answer 11 · 2026-04-02 04:56:26

34

Views

How do I write the formal proof?

Published on 02 Apr 2026 - 4:56

score 58 · Answer 12 · 2018-09-20 15:58:26

58

Views

Given a set $A$ and $n$ many $f_i$-ary functions $F_i$, the closure of a countable set $B$ under all the $F_i$'s is countable

Published on 20 Sep 2018 - 15:58

score 1k · Answer 13 · 2026-03-25 03:07:18

1k

Views

Diffeomorphism Implies Equality of Dimensions

Published on 25 Mar 2026 - 3:07

score 361 · Answer 14 · 2018-09-20 20:40:15

361

Views

find $A,B$ in way that $f:A\rightarrow B$ is bijective, when $f(x)=\sqrt{x^2-1}$

Published on 20 Sep 2018 - 20:40

score 248 · Answer 15 · 2018-09-20 21:01:57

248

Views

Prove that $P(A \cap B ) \geq 1 - P(\bar{A}) - P(\bar{B})$

Published on 20 Sep 2018 - 21:01

List Question

Prove formula $\operatorname{arctanh} x = \frac12\,\ln \left(\frac{1+x}{1-x}\right)$

Proof of an inequality using analytic geometry

On Stirling Number

How to obtain the quadratic equation when given that the sum of the roots at equal to 47 and the product of the roots is -59?

For Fibonacci numbers: $\gcd(F_m, F_n) = F_{\gcd(m, n)}$

Combinations with Conditional Probability

Solution to system of first order wave PDEs

Prove that $ I + J = R \iff b + J $ is invertible in $ R / J$, where $ I = \langle b \rangle$

Is the substitution of variables allowed in proofs?

Differentiability of the function $f(x,y)=\begin{cases} \frac{xy}{x^2+y^2}, & \text{if $(x,y)\ne(0,0)$}\\ 0, & \text{otherwise} \end{cases}$

How do I write the formal proof?

Given a set $A$ and $n$ many $f_i$-ary functions $F_i$, the closure of a countable set $B$ under all the $F_i$'s is countable

Diffeomorphism Implies Equality of Dimensions

find $A,B$ in way that $f:A\rightarrow B$ is bijective, when $f(x)=\sqrt{x^2-1}$

Prove that $P(A \cap B ) \geq 1 - P(\bar{A}) - P(\bar{B})$

Trending Questions

Popular # Hahtags

Popular Questions