Question

Find all $p\in\mathbb R[x]$ s.t. $p' \left(x^2\right)\cdot p'''(x)=3\cdot p''\left(x^2\right)\cdot x^2$

score 86 · Answer 1 · 2026-03-25 19:06:29

86

Views

Find all $p\in\mathbb R[x]$ s.t. $p' \left(x^2\right)\cdot p'''(x)=3\cdot p''\left(x^2\right)\cdot x^2$

Published on 25 Mar 2026 - 19:06

score 87 · Answer 2 · 2026-03-27 04:23:38

87

Views

Let $L$ be a Lie algebra. Is $Z(L) \subset [L,L]$?

Published on 27 Mar 2026 - 4:23

score 577 · Answer 3 · 2020-02-14 04:00:44

577

Views

Affine Hyperplane is Closed if and only if $f$ is continuous.

Published on 14 Feb 2020 - 4:00

score 276 · Answer 4 · 2026-03-28 04:33:36

276

Views

Proving that ${\rm Aut } G$ has an identity element

Published on 28 Mar 2026 - 4:33

score 35 · Answer 5 · 2020-02-14 10:08:18

35

Views

Show $\arctan(x+1) - \arctan(x) = \arctan(\frac{1}{x^2 + x +1})$

Published on 14 Feb 2020 - 10:08

score 966 · Answer 6 · 2026-03-25 12:53:57

966

Views

$X$ is compact iff every net in $X$ has a convergent subnet (using filters).

Published on 25 Mar 2026 - 12:53

score 134 · Answer 7 · 2026-03-26 14:28:17

134

Views

Swapping indices in cross product

Published on 26 Mar 2026 - 14:28

score 746 · Answer 8 · 2020-02-14 11:48:21

746

Views

UPDATED: If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, prove that $f(0) = 0.$

Published on 14 Feb 2020 - 11:48

score 212 · Answer 9 · 2026-04-01 11:53:19

212

Views

Second Countability $\implies$ Lindelöf property(Proof verification)

Published on 01 Apr 2026 - 11:53

score 182 · Answer 10 · 2020-02-14 14:17:29

182

Views

$140x^{.75}y^{.25}=213,415$ Find the rate of change of $x$ with respect to $y$ when $x=3000$ and $y=200$.

Published on 14 Feb 2020 - 14:17

score 62 · Answer 11 · 2026-03-26 01:35:00

62

Views

Proving that $p_I\circ h=p_I\circ h'$ implies $h=h'$

Published on 26 Mar 2026 - 1:35

score 66 · Answer 12 · 2026-03-25 23:56:42

66

Views

Proving that this set is a limit in $\mathbf{Set}$

Published on 25 Mar 2026 - 23:56

score 380 · Answer 13 · 2026-02-23 12:58:14

380

Views

Find the minimum number of zeros of $g(x)=(f'(x))^2+f(x)f''(x)$in the interval $[a, e]$ for the following given information.

Published on 23 Feb 2026 - 12:58

score 258 · Answer 14 · 2026-03-29 12:40:12

258

Views

What is $Var[A+B-2C]$?

Published on 29 Mar 2026 - 12:40

score 33 · Answer 15 · 2026-03-29 20:05:41

33

Views

Is any $m$-dimensional strict vector subspeace (so $m<p$) a rotational image of the Euclidean subspace $\mathbb{R}^m$?

Published on 29 Mar 2026 - 20:05

List Question

Find all $p\in\mathbb R[x]$ s.t. $p' \left(x^2\right)\cdot p'''(x)=3\cdot p''\left(x^2\right)\cdot x^2$

Let $L$ be a Lie algebra. Is $Z(L) \subset [L,L]$?

Affine Hyperplane is Closed if and only if $f$ is continuous.

Proving that ${\rm Aut } G$ has an identity element

Show $\arctan(x+1) - \arctan(x) = \arctan(\frac{1}{x^2 + x +1})$

$X$ is compact iff every net in $X$ has a convergent subnet (using filters).

Swapping indices in cross product

UPDATED: If $f(x + y) \leq yf(x) + f(f(x))$ for all real numbers $x$ and $y$, prove that $f(0) = 0.$

Second Countability $\implies$ Lindelöf property(Proof verification)

$140x^{.75}y^{.25}=213,415$ Find the rate of change of $x$ with respect to $y$ when $x=3000$ and $y=200$.

Proving that $p_I\circ h=p_I\circ h'$ implies $h=h'$

Proving that this set is a limit in $\mathbf{Set}$

Find the minimum number of zeros of $g(x)=(f'(x))^2+f(x)f''(x)$in the interval $[a, e]$ for the following given information.

What is $Var[A+B-2C]$?

Is any $m$-dimensional strict vector subspeace (so $m<p$) a rotational image of the Euclidean subspace $\mathbb{R}^m$?

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