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Algebra Question from Mathematics GRE

score 933 · Answer 1 · 2013-03-12 05:05:55

933

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Algebra Question from Mathematics GRE

Published on 12 Mar 2013 - 5:05

score 642 · Answer 2 · 2013-03-12 06:39:22

642

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Local Extrema of a 2D Surface in R^3 (Math GRE Question)

Published on 12 Mar 2013 - 6:39

score 31.2k · Answer 3 · 2013-03-30 02:49:51

31.2k

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Finding a number given its remainder when divided by other numbers

Published on 30 Mar 2013 - 2:49

score 140 · Answer 4 · 2020-09-29 22:27:23

140

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Is $\text{for}\ n\in \mathbb{N},\dfrac{u_{n+1}}{u_n}=q \iff \text{for}\ n\in \mathbb{N},u_{n+1}=q u_n$?

Published on 29 Sep 2020 - 22:27

score 291 · Answer 5 · 2021-03-16 07:52:56

291

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Let $P$ be a polynomial with integer coefficients satisfying $P(0)=1, P(1)=3, P'(0)=-1, P'(1)=10$. What is the minimum possible degree of $P$?

Published on 16 Mar 2021 - 7:52

score 44 · Answer 6 · 2021-03-22 09:12:30

44

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The order of $C=\sum_{k=0}^{90}(90-k)\cos(k ^{\circ}), S=\sum_{k=0}^{90}(90-k)\sin(k ^{\circ})$, and $T=\sum_{k=0}^{90}(90-k)\tan(k ^{\circ})$.

Published on 22 Mar 2021 - 9:12

score 226 · Answer 7 · 2021-05-15 04:47:27

226

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Possible dimensions of $V \cap W$ in $\mathbb{R}^n$

Published on 15 May 2021 - 4:47

score 756 · Answer 8 · 2021-05-17 06:16:23

756

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Let $h$ be the function defined by $h(x)=\int_{0}^{x^2}e^{x+t}dt$ for all real numbers $x$. Then $h'(1)=\dots$

Published on 17 May 2021 - 6:16

score 44 · Answer 9 · 2021-05-29 17:56:37

44

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$u=f(x,y)$ and the partial derivatives are themselves differentiable functions of $x$ and $y$ (Typo?)

Published on 29 May 2021 - 17:56

score 68 · Answer 10 · 2021-09-06 23:32:30

68

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Matrix in $M_2(\mathbf{R})$ of order $2$ has trace $0$

Published on 06 Sep 2021 - 23:32

score 212 · Answer 11 · 2021-10-22 15:48:50

212

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Showing that $AB$ is a subgroup.

Published on 22 Oct 2021 - 15:48

score 148 · Answer 12 · 2021-11-28 04:50:08

148

Views

If a $3\times 3$ matrix satisfies $A^3-A^2-A+I=0$, then it is not necessarily diagonalisable.

Published on 28 Nov 2021 - 4:50

score 36 · Answer 13 · 2022-01-17 16:21:00

36

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Finding relative extrema

Published on 17 Jan 2022 - 16:21

score 90 · Answer 14 · 2022-04-04 20:02:03

90

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If $f(x)=p \sin x + q x \cos x + x^2$ and $f(2)=3$, find $f(-2)$

Published on 04 Apr 2022 - 20:02

score 129 · Answer 15 · 2022-07-01 13:01:57

129

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How $5^{40} < 4^{60} < 27^{30}$, $8^{1/11} < 9^{1/10} < 10^{1/9}$, $e^{e} < \pi^{e} < e^{\pi}$, and $200^{100} < 200! < 100^{200}$?

Published on 01 Jul 2022 - 13:01

List Question

Algebra Question from Mathematics GRE

Local Extrema of a 2D Surface in R^3 (Math GRE Question)

Finding a number given its remainder when divided by other numbers

Is $\text{for}\ n\in \mathbb{N},\dfrac{u_{n+1}}{u_n}=q \iff \text{for}\ n\in \mathbb{N},u_{n+1}=q u_n$?

Let $P$ be a polynomial with integer coefficients satisfying $P(0)=1, P(1)=3, P'(0)=-1, P'(1)=10$. What is the minimum possible degree of $P$?

The order of $C=\sum_{k=0}^{90}(90-k)\cos(k ^{\circ}), S=\sum_{k=0}^{90}(90-k)\sin(k ^{\circ})$, and $T=\sum_{k=0}^{90}(90-k)\tan(k ^{\circ})$.

Possible dimensions of $V \cap W$ in $\mathbb{R}^n$

Let $h$ be the function defined by $h(x)=\int_{0}^{x^2}e^{x+t}dt$ for all real numbers $x$. Then $h'(1)=\dots$

$u=f(x,y)$ and the partial derivatives are themselves differentiable functions of $x$ and $y$ (Typo?)

Matrix in $M_2(\mathbf{R})$ of order $2$ has trace $0$

Showing that $AB$ is a subgroup.

If a $3\times 3$ matrix satisfies $A^3-A^2-A+I=0$, then it is not necessarily diagonalisable.

Finding relative extrema

If $f(x)=p \sin x + q x \cos x + x^2$ and $f(2)=3$, find $f(-2)$

How $5^{40} < 4^{60} < 27^{30}$, $8^{1/11} < 9^{1/10} < 10^{1/9}$, $e^{e} < \pi^{e} < e^{\pi}$, and $200^{100} < 200! < 100^{200}$?

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