HeroZhang001

Member for 10 months
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Henan, China

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calculus

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Answers

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Score Activity Newest

8

Use of $\sum_{r=1}^{\infty} \frac{1}{r^2} = \frac{\pi^2}{6} $ in evaluating $I$

May 14

8

Why $1− \frac12 + \frac13 − \frac14 + \frac15 - \cdots$ is not zero but $\ln2$

Jun 1

6

Product vs. join of subgroups of a finite group

Apr 27

4

Is there a sequence $a_n$ decreasing to $1$ such that $\sum n^{-a_n}$ converges?

Apr 28

4

Please tell me why my method of solving $\sin\left(\frac{\pi}{3}-2\,x\right)-\sin\left(6\,x\right)=2$ is not correct.

Jan 29

Questions

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Score Activity Newest Views

7

Assume $\int_0^\infty f(x)dx$ converges. Prove there exists $\xi\in[1,\infty)$ such that $\int_1^\infty \frac{f(x)}x dx=\int_1^\xi f(x)dx$.

Sep 3

4

Is $\{(\mathbb R,\phi)\}$ a smooth atlas for $\mathbb R$, where $\phi(x)=\left\{ \begin{array}{ll} x & x<0, \\ 2x& x\geq0~? \end{array} \right.$

Mar 1

4

Solution Verification: Compute $\int_{0}^{+\infty} \frac{\mathrm{e}^{-a x}-\mathrm{e}^{-b x}}{x} \sin x \mathrm{~d} x$, where $b>a>0$

Mar 5

3

Computing the De Rham Cohomology Group of Connected Sum $H_{\rm dR}^p(M_1 \# M_2)$

Dec 4, 2022

2

Proving the horizontal distribution is not involutive

Dec 14, 2022

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calculus

15

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8

posts

sequences-and-series

13

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3

posts

real-analysis

11

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6

posts

integration

9

Score

4

posts

group-theory

9

Score

2

posts

Reputation

+70

Assume $\int_0^\infty f(x)dx$ converges. Prove there exists $\xi\in[1,\infty)$ such that $\int_1^\infty \frac{f(x)}x dx=\int_1^\xi f(x)dx$.

+2

Find $f(\frac{2\pi k}{2^n \pm1})$ given $f(x)=\prod_{i=1}^{n-1}[2\cos(2^{i-1}x)-1],n\geq1$.

+10

Uniform continuity of the function $f(x)=x^a$

+10

Mathematical Analysis I by Zorich: show $f^{-1}(f(A)) \supset A$, $f(f^{-1}(B^{'})) \subset B'$

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