User experimentX - Mathematics Stack Exchange

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6

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votes

3

answers

449

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Evaluate:: $ 2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right) $

real-analysis sequences-and-series

feb 6 at 17:58 user17762 75.9k

5

10

votes

7

answers

1

kviews

How to solve an exponential equation with two different bases: $3^x - 2^x = 5$

calculus roots

jul 26 at 2:54 Rajesh K Singh 1,009

2

8

votes

2

answers

138

views

Evaluate: $\int_{0}^\infty e^{-x^2} \cos^n(x) dx $

improper-integrals

feb 23 at 12:31 Ayman Hourieh 11.1k

1

7

votes

3

answers

218

views

how to find this limit $\lim_{x\rightarrow 0} \frac{\sin x^2}{ \ln ( \cos x^2 \cos x + \sin x^2 \sin x)} = -2$ without using L'Hôpital's rule

trigonometry limit

aug 28 at 11:42 experimentX 3,513

1

6

votes

1

answer

459

views

Curl of a vector in spherical coordinates

multivariable-calculus

jun 21 '12 at 22:44 Jim Belk 13.7k

1

5

votes

2

answers

79

views

Evaluate: $\sum_{n=1}^{\infty}\frac{1}{n k^n}$

sequences-and-series

mar 31 at 11:20 Ragib Zaman 17.8k

2

5

votes

1

answer

172

views

Evaluate $\sum_{n=1}^{\infty} \frac{(2n)!}{2^{2n}(n!)^2 (2n-1)}$

sequences-and-series binomial-coefficients catalan-numbers

jan 22 at 19:50 Mike Spivey 25.8k

1

5

votes

1

answer

89

views

how to evaluate $ \int_0^\infty e^{- \left ( x - \frac a x \right )^2} dx $

improper-integrals

aug 29 at 7:52 sos440 13.7k

2

4

votes

3

answers

182

views

How to show that $1 \over \sqrt{1 - 4x} $ generate $\sum_{n=0}^\infty \binom{2n}{n}x^n $

sequences-and-series generating-functions

oct 2 at 11:55 Alfred Chern 922

4

votes

1

answer

173

views

response of unit step input in harmonically oscillating system

differential-equations

jun 7 '12 at 20:24 Rahul Narain 16.9k

1

3

votes

2

answers

93

views

Upper bound for $\displaystyle\int_1^\infty \frac{\lfloor x\rfloor }{x^3} dx $

definite-integral

feb 8 at 14:38 aziiri 648

3

votes

3

answers

237

views

how to show that $\int_0^\infty \sin(x^2) dx$ converges [duplicate]

real-analysis improper-integrals

jan 17 at 9:54 M. Strochyk 4,633

3

votes

3

answers

57

views

show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$

metric-spaces

dec 29 at 21:45 copper.hat 28.4k

2

3

votes

5

answers

1

kviews

How to prove $ \int_0^\infty e^{-x^2} \; dx = \frac{\sqrt{\pi}}2$ without changing into polar coordinates?

definite-integral

aug 29 at 8:58 Mhenni Benghorbal 13.8k

1

3

votes

1

answer

124

views

Find the integer solution of $ a^b = 2^{2 c + 1} + 2^c + 1 $

diophantine-equations

jul 25 at 21:35 anonymous 649

3

votes

3

answers

159

views

parametrization of surface element in surface integrals

integral surfaces

jun 19 '12 at 22:19 Nicholas Kirchner 596

3

votes

0

answers

88

views

Is it possible to evaluate this limit without series expansion and l'Hôpital's rule? [duplicate]

limit

jun 13 '12 at 16:22 Gigili 3,124

3

votes

2

answers

192

views

how to visualize binomial theorem geometrically?

combinatorics binomial-coefficients

jun 11 '12 at 14:09 Seth 867

1

2

votes

1

answer

79

views

for $|f (x_1) + … + f (x_n)| \le M$ how to prove that $S=\{ x\in [0,1]:f(x)\ne 0\}$ is countable?

analysis

jan 19 at 13:07 TonyK 11.8k

1

2

votes

2

answers

131

views

Solve $x^2 (a - bx) {d^2y \over dx^2} - x (5a - 4bx) {dy \over dx} + 3(2a - bx)y = 6a^2$

homework differential-equations

jan 16 at 8:06 doraemonpaul 2,993

1

2

votes

1

answer

128

views

hints on solving $ \sin^2 x {d^2y \over dx^2} = 2 y$

homework differential-equations

jul 27 at 18:57 Robert Israel 86k

1

2

votes

1

answer

307

views

invariance of cross product under coordinates rotation

homework coordinate-systems cross-product

jul 5 at 23:18 copper.hat 28.4k

2

votes

1

answer

28

views

gradient in polar coordinate by changing gradient in Cartesian coordinate

multivariable-calculus coordinate-systems polar-coordinates

jun 26 at 16:37 user17762 75.9k

2

votes

1

answer

147

views

surface integral of vector along the curved surface of cylinder

homework multivariable-calculus

jun 22 at 12:36 Christian Blatter 32.3k

2

votes

1

answer

134

views

How to arrive at Stokes's theorem from Green's theorem?

integral multivariable-calculus

jun 19 '12 at 20:51 Harald Hanche-Olsen 10.5k

2

votes

1

answer

605

views

transformation of unit vectors between coordinate systems

transformation

jun 15 '12 at 21:22 experimentX 3,513

2

votes

3

answers

1

kviews

proving gradient of a scalar field is perpendicular to equipotential surface

calculus vector-analysis

mar 19 '12 at 21:06 experimentX 3,513

1

vote

3

answers

86

views

how to show that the compactness of set implies closedness?

homework general-topology compactness

dec 30 at 12:04 Nameless 7,927

1

vote

2

answers

67

views

hints on solving DE

homework differential-equations

aug 2 at 12:20 Jayesh Badwaik 1,215

1

vote

2

answers

133

views

second order ODE via variation of parameters

differential-equations

jul 25 at 21:42 oen 7,433

experimentX

44 Questions