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liyushu
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4 votes
1 answer
45 views

Triple integral in spherical coordinate, where am I wrong

2 votes
1 answer
65 views

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

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 $x^2+y^2+z^2 \leq 1$

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} $

1 vote
4 answers
88 views

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

1 vote
1 answer
63 views

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

1 vote
0 answers
58 views

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

1 vote
0 answers
43 views

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

0 votes
0 answers
28 views

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

0 votes
0 answers
34 views

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

0 votes
1 answer
48 views

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

0 votes
1 answer
37 views

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

0 votes
1 answer
94 views

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

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

0 votes
0 answers
33 views

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

0 votes
2 answers
60 views

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

0 votes
1 answer
59 views

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

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 $x=0 \ y=0 \ x+y=1$

-1 votes
1 answer
27 views

Linearly independent numbers problem [duplicate]