User liyushu

4 votes

1 answer

45 views

Triple integral in spherical coordinate, where am I wrong

asked Nov 13, 2022 at 5:33

2 votes

1 answer

56 views

$\int _{2}^{+\infty }\ \dfrac{\sin x}{x\ln x }dx$ is convergent but not absolutely convergent

asked Apr 4, 2022 at 4:18

2 votes

1 answer

67 views

$\iiint\limits_{D}\frac{dxdydz}{\sqrt{x^2+y^2+(z-\frac{1}{2})^2} }$ D is given by $x^2+y^2+z^2 \leq 1$

asked Nov 11, 2022 at 10:17

1 vote

0 answers

38 views

$\forall x > 0$, there exists a unique $\xi_x$ s.t.$ \int_{0}^{x}e^{t^2}dt=xe^{\xi_x^2}$; solve $\lim_{x \to \infty} \frac{\xi_x}{x} $

asked Mar 22, 2022 at 4:29

1 vote

4 answers

87 views

Find area of $x^2+axy+y^2=1$, $|a|\leq1$

asked Mar 30, 2022 at 14:29

1 vote

1 answer

57 views

Show by strict application of the definition that the closure of $|z - z_0| < \delta$ is $|z - z_0| \leq \delta$.}

asked Apr 20 at 14:30

1 vote

0 answers

47 views

angles at the two points of intersection are opposite to each other.

asked Apr 24 at 13:38

1 vote

0 answers

39 views

Solution to the Partial Differential Equation $ u_t - xtu_x = 0 $

asked Sep 8 at 9:46

0 votes

0 answers

20 views

check the solution of the initial-boundary value problem (diffusion equation)

asked Nov 4 at 16:57

0 votes

0 answers

34 views

$\oint_{\Gamma}^{} (x^{\frac{4}{3}}+y^{\frac{4}{3}})ds,\Gamma \text{ is } x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$

asked Feb 14 at 14:12

0 votes

1 answer

46 views

integral in the question Sign of remainder in series for $cos$ and $sin$

asked Apr 14 at 9:09

0 votes

1 answer

35 views

integral inequality in the question Sign of remainder in series for $\cos$ and $\sin$

asked Apr 15 at 8:38

0 votes

1 answer

88 views

$\int _{1}^{+\infty }\sin\left( \dfrac{\sin x}{x}\right) dx$ is convergent but not absolutely convergent

asked Mar 31, 2022 at 14:30

0 votes

2 answers

57 views

prove that $\int_{0}^{1} \frac{\sin \frac{1}{x}}{x^{\frac{3}{2}} \ln \left(1+\frac{1}{x}\right)} \mathrm{d} x $ is convergent

asked Apr 5, 2022 at 13:57

0 votes

0 answers

33 views

K is an infinite field, f is a nonzero polynomial, prove $\exists \alpha_1,\cdots ,\alpha_n \> \in \mathbb{K}\>s.t. f(\alpha_1,\cdots ,\alpha_n)\neq0$

asked Apr 6, 2022 at 6:35

0 votes

2 answers

60 views

$\prod_{n=3 }^{+\infty} \cos\frac{\pi}{n}$is convergent or not?

asked Apr 27, 2022 at 3:46

0 votes

1 answer

48 views

How to use Cauchy Hadamard's Theorem in the case of irregular footmarks and exponents

asked May 14, 2022 at 11:39

0 votes

0 answers

20 views

evaluating double integral $\iint\limits_{D} \cos \left ( \frac{x-y}{x+y} \right ) dxdy$ D is a bounded closed area given by $x=0 \ y=0 \ x+y=1$

asked Nov 7, 2022 at 10:49

-1 votes

1 answer

27 views

Linearly independent numbers problem [duplicate]

asked Dec 27, 2021 at 4:25

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19 Questions

Triple integral in spherical coordinate, where am I wrong

$\int _{2}^{+\infty }\ \dfrac{\sin x}{x\ln x }dx$ is convergent but not absolutely convergent

$\iiint\limits_{D}\frac{dxdydz}{\sqrt{x^2+y^2+(z-\frac{1}{2})^2} }$ D is given by $x^2+y^2+z^2 \leq 1$

$\forall x > 0$, there exists a unique $\xi_x$ s.t.$ \int_{0}^{x}e^{t^2}dt=xe^{\xi_x^2}$; solve $\lim_{x \to \infty} \frac{\xi_x}{x} $

Find area of $x^2+axy+y^2=1$, $|a|\leq1$

Show by strict application of the definition that the closure of $|z - z_0| < \delta$ is $|z - z_0| \leq \delta$.}

angles at the two points of intersection are opposite to each other.

Solution to the Partial Differential Equation $ u_t - xtu_x = 0 $

check the solution of the initial-boundary value problem (diffusion equation)

$\oint_{\Gamma}^{} (x^{\frac{4}{3}}+y^{\frac{4}{3}})ds,\Gamma \text{ is } x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$

integral in the question Sign of remainder in series for $cos$ and $sin$

integral inequality in the question Sign of remainder in series for $\cos$ and $\sin$

$\int _{1}^{+\infty }\sin\left( \dfrac{\sin x}{x}\right) dx$ is convergent but not absolutely convergent

prove that $\int_{0}^{1} \frac{\sin \frac{1}{x}}{x^{\frac{3}{2}} \ln \left(1+\frac{1}{x}\right)} \mathrm{d} x $ is convergent

K is an infinite field, f is a nonzero polynomial, prove $\exists \alpha_1,\cdots ,\alpha_n \> \in \mathbb{K}\>s.t. f(\alpha_1,\cdots ,\alpha_n)\neq0$

$\prod_{n=3 }^{+\infty} \cos\frac{\pi}{n}$is convergent or not?

How to use Cauchy Hadamard's Theorem in the case of irregular footmarks and exponents

evaluating double integral $\iint\limits_{D} \cos \left ( \frac{x-y}{x+y} \right ) dxdy$ D is a bounded closed area given by $x=0 \ y=0 \ x+y=1$

Linearly independent numbers problem [duplicate]