User shangq_tou

7 votes

1 answer

146 views

limit of two entirely different sequences

sequences-and-series limits

asked Apr 8, 2021 at 12:03

6 votes

2 answers

194 views

$\int _0^1f^2\left(x\right)dx-2\int _0^{\sqrt{3}-1}\:\left(x+1\right)f\left(x\right)dx\:+1=0$

asked May 17 at 10:33

5 votes

1 answer

172 views

$c_n=a^n-b^n$, $S=\{c_1,c_2,...\}$ is finite then $0 \in S$

abstract-algebra ring-theory

asked May 14 at 17:32

5 votes

3 answers

153 views

Evaluate $\lim_{n\to\infty}\int_1^n\frac{\ln x}{c_n+x\ln x}\,dx$

real-analysis limits

asked Apr 30 at 19:52

5 votes

2 answers

116 views

Let $f_n$ be a$f_{n+1}\left(x\right)=\frac{1}{x}\int _0^xf_n\left(t\right)dt\:$

functional-analysis

asked May 14 at 11:34

4 votes

2 answers

148 views

Area under the function $f$

real-analysis

asked Nov 1, 2021 at 13:19

4 votes

3 answers

111 views

matrices such that $A^2B+BA^2=2ABA$

linear-algebra

asked Mar 27, 2021 at 13:11

4 votes

5 answers

90 views

A quite difficult limit: $\lim _{x\to 0}\frac{\exp(x^2)-\cos x-x\sin x}{\sinh^2x}$

limits taylor-expansion

asked Feb 8, 2021 at 10:44

3 votes

1 answer

69 views

$f(x)=a_1\sin x+a_2\sin 2x+a_3\sin 3x+...+a_n\sin nx$

real-analysis

asked Jul 1, 2021 at 11:54

3 votes

2 answers

309 views

binary matrix and product between a matrix and its transpose

linear-algebra

asked Aug 11, 2021 at 10:51

2 votes

1 answer

65 views

limit of sums of integer parts

limits

asked Aug 11, 2021 at 9:24

2 votes

1 answer

126 views

prove that $x^6=(ax)^3$ implies $x^3=e,\: \forall x\in G$

group-theory

asked Jul 1, 2021 at 15:05

2 votes

1 answer

356 views

About char and $x+x=0$

abstract-algebra ring-theory

asked Mar 10 at 18:16

2 votes

2 answers

115 views

$\lim_{n\to \infty}\left( \int_0^1 (Q(x))^ndx\right)^{\frac{1}{n}}$

integration limits definite-integrals

asked Mar 10 at 18:43

2 votes

1 answer

112 views

elements of order 2 in a ring

abstract-algebra ring-theory

asked Mar 22 at 21:45

2 votes

2 answers

221 views

primitive of a function with $e$ and trigonometric functions

real-analysis integration definite-integrals indefinite-integrals

asked Mar 29 at 16:53

2 votes

0 answers

89 views

Find the total number of roots of a certain polynomial [closed]

real-analysis polynomials roots

asked Mar 29 at 21:53

2 votes

2 answers

83 views

Second Order Differential Equations $ay''+by'+cy=0$, without complex numbers

real-analysis ordinary-differential-equations

asked Dec 11, 2021 at 9:19

1 vote

2 answers

212 views

Ring with three idempotents satisfying $\alpha+ \beta+ \gamma=0$. Prove that $\alpha=\beta= \gamma$.

abstract-algebra ring-theory proof-explanation noncommutative-algebra

asked Feb 26 at 12:34

1 vote

1 answer

80 views

$\int _a^bQ(x)\cdot w(x)dx=0$

real-analysis integration polynomials definite-integrals

asked Mar 10 at 13:03

1 vote

0 answers

63 views

$x_{n+1}=\sum_{k=1}^{n-1}a_{(n,k)}x_k $, $S=\{x_1,x_2,...\}$ is finite then $0 \in S$

abstract-algebra ring-theory

asked May 14 at 13:05

1 vote

1 answer

139 views

beta and gamma helping solve an integral

real-analysis integration definite-integrals

asked Mar 31 at 21:06

1 vote

2 answers

111 views

the composition of two functions that have primitives has primitives

real-analysis integration

asked Jul 1, 2021 at 18:29

1 vote

1 answer

91 views

local extrema of a Continuous function

continuity

asked Feb 28, 2021 at 22:01

1 vote

1 answer

68 views

Finding the determinant of a $n\times n$ matrix of rational functions

matrices determinant

asked Mar 5, 2021 at 13:34

1 vote

0 answers

80 views

Knowing the fact that $A^2B=A^2-B$

linear-algebra

asked Mar 5, 2021 at 20:37

1 vote

1 answer

62 views

$A^{2m+1}=A+I_n$ then $\det(A)>0$

linear-algebra

asked Mar 6, 2021 at 19:11

1 vote

1 answer

98 views

How to find the determinant of a matrix of sines and cosines?

matrices determinant

asked Mar 7, 2021 at 14:34

1 vote

1 answer

38 views

Is this true for integers matrices $A=XA’Y$

matrices

asked Mar 25, 2021 at 8:02

1 vote

0 answers

31 views

impossible rank equality

linear-algebra matrix-rank

asked Mar 14, 2021 at 22:12

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48 Questions

limit of two entirely different sequences

$\int _0^1f^2\left(x\right)dx-2\int _0^{\sqrt{3}-1}\:\left(x+1\right)f\left(x\right)dx\:+1=0$

$c_n=a^n-b^n$, $S=\{c_1,c_2,...\}$ is finite then $0 \in S$

Evaluate $\lim_{n\to\infty}\int_1^n\frac{\ln x}{c_n+x\ln x}\,dx$

Let $f_n$ be a$f_{n+1}\left(x\right)=\frac{1}{x}\int _0^xf_n\left(t\right)dt\:$

Area under the function $f$

matrices such that $A^2B+BA^2=2ABA$

A quite difficult limit: $\lim _{x\to 0}\frac{\exp(x^2)-\cos x-x\sin x}{\sinh^2x}$

$f(x)=a_1\sin x+a_2\sin 2x+a_3\sin 3x+...+a_n\sin nx$

binary matrix and product between a matrix and its transpose

limit of sums of integer parts

prove that $x^6=(ax)^3$ implies $x^3=e,\: \forall x\in G$

About char and $x+x=0$

$\lim_{n\to \infty}\left( \int_0^1 (Q(x))^ndx\right)^{\frac{1}{n}}$

elements of order 2 in a ring

primitive of a function with $e$ and trigonometric functions

Find the total number of roots of a certain polynomial [closed]

Second Order Differential Equations $ay''+by'+cy=0$, without complex numbers

Ring with three idempotents satisfying $\alpha+ \beta+ \gamma=0$. Prove that $\alpha=\beta= \gamma$.

$\int _a^bQ(x)\cdot w(x)dx=0$

$x_{n+1}=\sum_{k=1}^{n-1}a_{(n,k)}x_k $, $S=\{x_1,x_2,...\}$ is finite then $0 \in S$

beta and gamma helping solve an integral

the composition of two functions that have primitives has primitives

local extrema of a Continuous function

Finding the determinant of a $n\times n$ matrix of rational functions

Knowing the fact that $A^2B=A^2-B$

$A^{2m+1}=A+I_n$ then $\det(A)>0$

How to find the determinant of a matrix of sines and cosines?

Is this true for integers matrices $A=XA’Y$

impossible rank equality