Mathematics Stack Exchange

61

votes

10

answers

3

kviews

How can I find the surface area of a normal chicken egg?

calculus geometry

jun 1 at 5:20 Ｊ. M. 39.7k

23

votes

8

answers

1

kviews

explaining the derivative of $x^x$

calculus teaching fake-proofs

may 30 at 14:59 sav 54

19

votes

4

answers

858

views

Find $\lim\limits_{n \rightarrow \infty}\dfrac{\sin 1+2\sin \frac{1}{2}+\cdots+n\sin \frac{1}{n}}{n}$

calculus limit

may 13 at 17:45 Cortizol 1,418

29

votes

4

answers

890

views

When $f(x+1)-f(x)=f'(x)$, what are the solutions for $f(x)$?

calculus analysis functions

may 13 at 1:20 newzad 297

28

votes

5

answers

419

views

Closed form for $\prod_{n=1}^\infty\sqrt[2^n]{\frac{\Gamma(2^n+\frac{1}{2})}{\Gamma(2^n)}}$

calculus combinatorics gamma-function closed-form infinite-product

may 13 at 14:14 robjohn♦ 61.9k

12

votes

4

answers

297

views

Which methods to use to integrate $\int{\frac{x^4 + 1}{x^2 +1}}\, dx$

calculus integral integration

may 21 at 4:02 lab bhattacharjee 30.7k

13

votes

1

answer

204

views

Is it possible to simplify $\frac{\Gamma\left(\frac{1}{10}\right)}{\Gamma\left(\frac{2}{15}\right)\ \Gamma\left(\frac{7}{15}\right)}$?

calculus special-functions gamma-function

may 31 at 4:23 Ron Gordon 28.8k

13

votes

3

answers

168

views

Prove that If $f$ is polynomial function of even degree $n$ with always $f\geq0$ then $f+f'+f''+\cdots+f^{(n)}\geq 0$.

calculus polynomials

9h ago Daniel Margolis 9

23

votes

2

answers

241

views

$\int_0^{\infty}\frac{x^3}{(x^4+1)(e^x-1)}\mathrm dx$

calculus integral definite-integral improper-integrals closed-form

may 17 at 16:45 Vladimir Reshetnikov 2,206

15

votes

3

answers

182

views

$\sum_{n=1}^\infty(n\ \text{arccot}\ n-1)$

calculus sequences-and-series trigonometry summation closed-form

may 17 at 2:31 Vladimir Reshetnikov 2,206

23

votes

4

answers

310

views

+150

Improper integral diverges

calculus real-analysis improper-integrals

1d ago user72694 1,191

10

votes

2

answers

250

views

What is wrong with this fake proof that $\lim\limits_{n\rightarrow \infty}\sqrt[n]{n!} = 1$?

calculus sequences-and-series limit fake-proofs

may 30 at 13:40 MJD 21.3k

4

votes

8

answers

151

views

Limit of $\lim_{x \to 0}\left (x\cdot \sin\left(\dfrac{1}{x}\right)\right)$ is $0$ or $1$?

calculus limit

may 17 at 17:47 King of Coding 1

17

votes

2

answers

237

views

Closed form for $\sum_{n=1}^\infty\frac{1}{2^n\left(1+\sqrt[2^n]{2}\right)}$

calculus sequences-and-series closed-form

may 15 at 10:38 Ron Gordon 28.8k

10

votes

2

answers

270

views

How to show that $\sqrt{1+\sqrt{2+\sqrt{3+\cdots+\sqrt{2006}}}}<2$

calculus

may 28 at 11:44 L. F. 3,801

14

votes

3

answers

163

views

Find the value of $\int_{0}^{\infty}\frac{x^3}{e^x-1}\ln(e^x - 1)\,dx$

calculus integral special-functions definite-integral riemann-zeta

may 21 at 13:50 Mhenni Benghorbal 15.1k

16

votes

4

answers

307

views

Finding the fraction $\frac{a^5+b^5+c^5+d^5}{a^6+b^6+c^6+d^6}$ when knowing the sums $a+b+c+d$ to $a^4+b^4+c^4+d^4$

calculus

may 28 at 4:30 Inceptio 5,156

6

votes

5

answers

143

views

Evaluating the series $\sum\limits_{n=1}^\infty \frac1{4n^2+2n}$

calculus real-analysis sequences-and-series

may 31 at 10:03 Mhenni Benghorbal 15.1k

25

votes

1

answer

319

views

Finding the sum- $x+x^{2}+x^{4}+x^{8}+x^{16}\cdots$

calculus sequences-and-series recurrence-relations summation

may 28 at 15:03 Mathlover 3,220

11

votes

4

answers

273

views

Good calculus exercises/problems?

calculus reference-request exercises-and-solutions

may 27 at 7:56 Shaan Shrestha 1

8

votes

5

answers

184

views

Matrices with eigenvalues 0 and 1

calculus linear-algebra matrices eigenvalues

may 10 at 22:49 Sammy Black 2,841

18

votes

4

answers

225

views

$\int_0^\pi\frac{3\cos x+\sqrt{8+\cos^2 x}}{\sin x}x\ \mathrm dx$

calculus trigonometry special-functions definite-integral closed-form

may 17 at 4:01 oen 7,820

3

votes

5

answers

131

views

How to show $\int_{0}^\infty e^{x^2}dx$ does not converge?

calculus

jun 1 at 2:15 Michael Hardy 50.1k

4

votes

4

answers

127

views

Differentiate $\log_{10}x$

calculus derivatives logarithms

may 15 at 5:54 iostream007 1,742

8

votes

2

answers

174

views

Evaluating $\int_{0}^{1} \frac{ \ln x \ln (1-x)}{\sqrt{x} \sqrt{1-x}} dx$

calculus integral integration

may 31 at 5:34 Ｊ. M. 39.7k

9

votes

2

answers

158

views

$\cos(x)+\cos(x\sqrt{2})$ is not periodic

calculus functions trigonometry periodic-functions

may 13 at 11:17 Ralph Tandetzky 516

4

votes

6

answers

147

views

What does $\lim\limits_{x\to\pi/6}\frac{1-\sqrt{3}\tan x}{\pi-6x}$ evaluate to?

calculus limit trigonometry

jun 1 at 17:03 iostream007 1,742

5

votes

4

answers

154

views

Example for Riemann integrable function such that $\int^{a+1}_a f(x)dx=0$ but $ f(x)\neq 0$

calculus integral

may 11 at 22:40 Dr H 69

7

votes

4

answers

191

views

How prove this $\int_{0}^{\infty}\sin{x}\sin{\sqrt{x}}dx=\dfrac{\sqrt{\pi}}{2}\sin{\left(\dfrac{3\pi-1}{4}\right)}$

calculus integral

may 24 at 1:40 sos440 15.8k

10

votes

4

answers

183

views

Solving $\int_0^{\infty} \sin(ax^2)\sin(b/x^2)\,\mathrm dx$

calculus definite-integral improper-integrals

jun 1 at 14:37 L. F. 3,801

3

votes

5

answers

207

views

Why isn't this limit equal to $0$?

calculus limit

may 10 at 19:40 amWhy 58.8k

22

votes

1

answer

183

views

Closed form for $\prod_{n=1}^\infty\sqrt[2^n]{\tanh(2^n)},$

calculus closed-form infinite-product hyperbolic-functions trigonometric-series

may 13 at 4:11 Escargot 176

6

votes

3

answers

128

views

Integrating $\ln x$ by parts

homework calculus

jun 3 at 14:53 Michael Hardy 50.1k

3

votes

7

answers

202

views

Why isn't the derivative of $e^x$ equal to $xe^{(x-1)}$?

calculus derivatives

may 27 at 20:03 Kaz 2,389

3

votes

5

answers

147

views

How to integrate $\int \sqrt{x^2+a^2}dx$

calculus real-analysis integration

may 29 at 9:45 iostream007 1,742

5

votes

4

answers

158

views

Finding another way of doing this integral $\sqrt{\frac{1-\sqrt{x}}{1+\sqrt{x}}}$

calculus integration

jun 3 at 6:04 Ayush Khaitan 248

7

votes

2

answers

137

views

How can I see if this integral is convergent or not $\int_0^\infty \ \frac{1}{1 + x^4\sin x} \,dx $

calculus improper-integrals

may 13 at 20:50 robjohn♦ 61.9k

10

votes

3

answers

137

views

Closed form for n-th anti-derivative of $\log x$

calculus integral logarithms closed-form

may 24 at 6:21 Mhenni Benghorbal 15.1k

5

votes

5

answers

98

views

How to determine the image of a set?

calculus

may 11 at 13:00 Mark McClure 3,316

6

votes

3

answers

155

views

Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$

calculus limit

may 24 at 18:18 Michael Hardy 50.1k

15

votes

1

answer

193

views

Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$

calculus integral logarithms definite-integral closed-form

may 14 at 14:11 O.L. 6,023

6

votes

3

answers

117

views

Integral of $\cot^2 x$?

calculus integral integration indefinite-integral

may 26 at 8:47 Américo Tavares 21.2k

10

votes

2

answers

212

views

Notation: Why write the differential first?

calculus notation

may 10 at 15:32 Sharkos 5,938

5

votes

5

answers

122

views

Limit as $x$ approaches $1$ from the right of $\frac{1}{\ln x}-\frac{1}{x-1}$

calculus limit

may 18 at 16:51 sos440 15.8k

4

votes

3

answers

107

views

Limit. $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}.$

calculus analysis limit

may 19 at 19:02 hmedan.mnsh 544

8

votes

2

answers

129

views

How to prove $4\times{_2F_1}(-1/4,3/4;7/4;(2-\sqrt3)/4)-{_2F_1}(3/4,3/4;7/4;(2-\sqrt3)/4)\stackrel?=\frac{3\sqrt[4]{2+\sqrt3}}{\sqrt2}$

calculus special-functions closed-form conjectures hypergeometric-function

may 24 at 7:48 O.L. 6,023

3

votes

5

answers

86

views

Calculate the limit: $\lim_{n\to+\infty}\sum_{k=1}^n\frac{\sin{\frac{k\pi}n}}{n}$ Using definite integral between the interval $[0,1]$.

calculus integral definite-integral

may 25 at 17:04 Alex 3,481

4

votes

3

answers

179

views

Why the $\nabla f(x)$ in the direction orthogonal to $f(x)$?

calculus derivatives

may 31 at 20:41 Elias 3,191

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