User Milan - Mathematics Stack Exchange

28 votes

4 answers

6k views

Is the proof of Pythagorean theorem using dot (inner) product circular?

asked Feb 14, 2019 at 17:55

12 votes

2 answers

259 views

How to show $\int_0^\infty\frac1{(1+x^2)(1+x^p)}$ doesn't depend on $p$?

asked Jun 16, 2020 at 12:21

7 votes

1 answer

148 views

Is $\lim\limits_{n\to\infty}\Bigl(\frac{2+\sin n}{3}\Bigr)^n =0 $; $n \in \mathbb{N}$?

asked Aug 28, 2019 at 17:09

6 votes

4 answers

541 views

$\int_0^1f(x) dx =0$, $\int_0^1xf(x) dx =0$. How to show that f has at least two zeros?

asked Jun 27, 2020 at 9:30

5 votes

4 answers

230 views

Why does fundamental theorem of calculus not work for this integral $\int_0^{2\pi}\frac{dx}{(3+\cos x)(2+\cos x)}$?

asked Apr 28, 2020 at 15:18

4 votes

2 answers

1k views

Prove there exists $\xi$ such that $f(\xi)=f(a)+f'(\xi)(b-a) $

asked Jan 16, 2020 at 17:16

3 votes

0 answers

268 views

$|A|\le |B| $implies$ |P(A)|\le|P(B)| $

asked Oct 24, 2019 at 16:51

3 votes

1 answer

497 views

$ Av=\lambda v \implies\ A^*v=\overline \lambda v $, Is this true only for normal operators?

asked Feb 6, 2019 at 20:02

3 votes

3 answers

285 views

How to derive $ \frac ab -x= \frac {c-xd}{b}+\left(\frac{b-d}{b}\right) \left(\frac{a-c}{b-d} - x \right) $

asked Aug 13, 2019 at 16:01

3 votes

1 answer

324 views

Is the identity scalar axiom needed for the proof that $0\cdot v=\mathbf{0}$

asked Nov 28, 2019 at 18:46

3 votes

2 answers

178 views

If $\lim \limits_{x \to a}\left(f(x)+\frac{1}{f(x)}\right)=2,$ then $\lim \limits_{x \to a}f(x)=1$ [duplicate]

asked Jan 3, 2020 at 21:38

3 votes

2 answers

419 views

Can every function be represented as $ e^{kx} $

asked Mar 29, 2019 at 19:56

2 votes

1 answer

39 views

Is this system of differential equations coupled or not?

asked Mar 8, 2019 at 17:20

2 votes

1 answer

63 views

$\lim_{n\to \infty} \frac{(-1)^{\frac{(n-1)(n-2)}{2} }}{n} $, solving this limit using Stolz theorem and getting the wrong result

asked Oct 27, 2018 at 18:10

2 votes

2 answers

319 views

Changing order of partial sum and integral all under limit to infinity

asked Jan 26, 2019 at 18:58

2 votes

1 answer

658 views

Generalized polar coordinates, how to switch form cartesian to polar

asked Jul 19, 2018 at 13:55

2 votes

2 answers

185 views

Area bounded by $(\sqrt{|x|}+\sqrt{|y|})^{12}=xy$ , how to convert this to polar equation, what to do with absolute values?

asked Jul 21, 2018 at 17:14

2 votes

1 answer

287 views

Finding the rank of matrix that has a parameter

asked Aug 18, 2018 at 17:02

2 votes

4 answers

222 views

Where is the mistake ( in using mean value theorem)?

asked Dec 31, 2019 at 11:41

2 votes

4 answers

376 views

$\tan x>x+\frac {x^3}3$ for $x\in(0,\frac\pi2)$

asked Jan 1, 2020 at 13:32

2 votes

2 answers

70 views

Find $\lim_{x \to \infty} \left({\frac{x^k}{1+x+...+x^k}}\right)^{1+2x}$

asked Dec 17, 2019 at 16:21

2 votes

0 answers

64 views

Is this a valid way to solve $\lim_{x \to \infty} \frac{\log({x^2-x+1)}}{\log{(x^{10}+x^5+1)}}$

asked Dec 17, 2019 at 17:28

2 votes

2 answers

106 views

Find all $x$ such that determinant is zero .

asked Nov 24, 2019 at 21:35

2 votes

1 answer

903 views

Basis of space of arithmetic sequences

asked Jan 19, 2020 at 11:08

2 votes

2 answers

184 views

$\sum_{n=1}^\infty\frac{(-1)^n\sin ^2n}{n}$ Is the following solution wrong ?; Does $\sum\frac{(-1)^n\cos 2n}{2n}$ converge?

asked Jun 18, 2020 at 10:03

1 vote

3 answers

124 views

Why is $\int_0^{{9\pi}\over{4}}{1 \over |\sin x|+|\cos x| }dx~ = ~9\int_0^{{\pi}\over{4}}{1 \over |\sin x|+|\cos x| }dx$?

asked May 19, 2020 at 18:26

1 vote

1 answer

105 views

Why is $\sum a_nf(n) = \int_0^xf(t)~d(A(t))$?

asked Sep 5, 2020 at 11:14

1 vote

2 answers

93 views

Is it always possible to partition data in such a way that Simpson's paradox is achieved?

asked Sep 12, 2020 at 20:15

1 vote

0 answers

30 views

Solution verification: $f(x)=\frac{x^2}{(x^3-4)^{\frac13}}$ series expansion at positive and negative $\infty$

asked Jan 25, 2020 at 15:12

1 vote

1 answer

49 views

How to find limit of $a_n=\int_n^{n+1}f(x) $ where $(\forall x\ge0) 0<f(x+1)<f(x) ~\text{and} \lim_{x\to\infty}f(x)=0$

asked May 7, 2020 at 11:25

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59 Questions

Is the proof of Pythagorean theorem using dot (inner) product circular?

How to show $\int_0^\infty\frac1{(1+x^2)(1+x^p)}$ doesn't depend on $p$?

Is $\lim\limits_{n\to\infty}\Bigl(\frac{2+\sin n}{3}\Bigr)^n =0 $; $n \in \mathbb{N}$?

$\int_0^1f(x) dx =0$, $\int_0^1xf(x) dx =0$. How to show that f has at least two zeros?

Why does fundamental theorem of calculus not work for this integral $\int_0^{2\pi}\frac{dx}{(3+\cos x)(2+\cos x)}$?

Prove there exists $\xi$ such that $f(\xi)=f(a)+f'(\xi)(b-a) $

$|A|\le |B| $implies$ |P(A)|\le|P(B)| $

$ Av=\lambda v \implies\ A^*v=\overline \lambda v $, Is this true only for normal operators?

How to derive $ \frac ab -x= \frac {c-xd}{b}+\left(\frac{b-d}{b}\right) \left(\frac{a-c}{b-d} - x \right) $

Is the identity scalar axiom needed for the proof that $0\cdot v=\mathbf{0}$

If $\lim \limits_{x \to a}\left(f(x)+\frac{1}{f(x)}\right)=2,$ then $\lim \limits_{x \to a}f(x)=1$ [duplicate]

Can every function be represented as $ e^{kx} $

Is this system of differential equations coupled or not?

$\lim_{n\to \infty} \frac{(-1)^{\frac{(n-1)(n-2)}{2} }}{n} $, solving this limit using Stolz theorem and getting the wrong result

Changing order of partial sum and integral all under limit to infinity

Generalized polar coordinates, how to switch form cartesian to polar

Area bounded by $(\sqrt{|x|}+\sqrt{|y|})^{12}=xy$ , how to convert this to polar equation, what to do with absolute values?

Finding the rank of matrix that has a parameter

Where is the mistake ( in using mean value theorem)?

$\tan x>x+\frac {x^3}3$ for $x\in(0,\frac\pi2)$

Find $\lim_{x \to \infty} \left({\frac{x^k}{1+x+...+x^k}}\right)^{1+2x}$

Is this a valid way to solve $\lim_{x \to \infty} \frac{\log({x^2-x+1)}}{\log{(x^{10}+x^5+1)}}$

Find all $x$ such that determinant is zero .

Basis of space of arithmetic sequences

$\sum_{n=1}^\infty\frac{(-1)^n\sin ^2n}{n}$ Is the following solution wrong ?; Does $\sum\frac{(-1)^n\cos 2n}{2n}$ converge?

Why is $\int_0^{{9\pi}\over{4}}{1 \over |\sin x|+|\cos x| }dx~ = ~9\int_0^{{\pi}\over{4}}{1 \over |\sin x|+|\cos x| }dx$?

Why is $\sum a_nf(n) = \int_0^xf(t)~d(A(t))$?

Is it always possible to partition data in such a way that Simpson's paradox is achieved?

Solution verification: $f(x)=\frac{x^2}{(x^3-4)^{\frac13}}$ series expansion at positive and negative $\infty$

How to find limit of $a_n=\int_n^{n+1}f(x) $ where $(\forall x\ge0) 0<f(x+1)<f(x) ~\text{and} \lim_{x\to\infty}f(x)=0$