Question

Prove that $x^3 - 3x + c$ has at most one root in $[0,1]$, no matter what $c$ may be

score 420 · Answer 1 · 2022-09-16 02:23:14

420

Views

Prove that $x^3 - 3x + c$ has at most one root in $[0,1]$, no matter what $c$ may be

Published on 16 Sep 2022 - 2:23

score 101 · Answer 2 · 2022-09-27 12:52:01

101

Views

Elementary closed form of $\exp\left(b\int_0^x \frac{t^{a-1}}{1-t^b}dt\right);a,b\in\Bbb N$

Published on 27 Sep 2022 - 12:52

score 70 · Answer 3 · 2022-10-03 13:41:01

70

Views

Domain of the $f(x) = \sqrt{x}$

Published on 03 Oct 2022 - 13:41

score 124 · Answer 4 · 2022-10-08 06:09:43

124

Views

Classification of integrals not expressible in elementary functions?

Published on 08 Oct 2022 - 6:09

score 58 · Answer 5 · 2022-10-17 17:15:10

58

Views

Why are "Most" integrals of elementary functions themselves not elementary functions?

Published on 17 Oct 2022 - 17:15

score 91 · Answer 6 · 2022-10-23 22:18:19

91

Views

When exactly must two elementary functions be identical if they are sufficiently close?

Published on 23 Oct 2022 - 22:18

score 473 · Answer 7 · 2022-11-12 02:42:35

473

Views

But is it really true that $\log(xy) = \log(x)+\log(y)$

Published on 12 Nov 2022 - 2:42

score 537 · Answer 8 · 2022-11-16 20:55:11

537

Views

Center of mass of a circular arc of radius R subtending an angle at the center

Published on 16 Nov 2022 - 20:55

score 174 · Answer 9 · 2022-11-27 20:01:01

174

Views

How can we show that $A(z,e^z)$ and $A(\ln (z),z)$ have no elementary inverse?

Published on 27 Nov 2022 - 20:01

score 29 · Answer 10 · 2022-11-30 11:05:18

29

Views

Equivalence between $f(x)e^g(x)$ being integrable and $r'(x) +g'(x)r(x)=f(x)$ having a function $r(x)$ that solves it.

Published on 30 Nov 2022 - 11:05

score 164 · Answer 11 · 2022-12-19 20:31:36

164

Views

What are the closed-form inverses of $x \sinh(x), x \cosh(x), x \tanh(x), x\ \text{sech}(x), x \coth(x), x\ \text{csch}(x)$?

Published on 19 Dec 2022 - 20:31

score 96 · Answer 12 · 2022-12-21 22:40:53

96

Views

Very trivial doubt on fractional exponents.

Published on 21 Dec 2022 - 22:40

score 103 · Answer 13 · 2022-12-22 18:00:20

103

Views

What are the closed-form inverses of $x+\sinh(x)$, $x+\cosh(x)$?

Published on 22 Dec 2022 - 18:00

score 455 · Answer 14 · 2022-12-24 11:05:38

455

Views

Calculating $\frac{1.01^5}{1.01^5-1}$ without calculator with good accuracy?

Published on 24 Dec 2022 - 11:05

score 208 · Answer 15 · 2022-12-31 18:10:54

208

Views

Given an arbitrary composite elementary function, does there exist some method to give us an intuition of its graph?

Published on 31 Dec 2022 - 18:10

List Question

Prove that $x^3 - 3x + c$ has at most one root in $[0,1]$, no matter what $c$ may be

Elementary closed form of $\exp\left(b\int_0^x \frac{t^{a-1}}{1-t^b}dt\right);a,b\in\Bbb N$

Domain of the $f(x) = \sqrt{x}$

Classification of integrals not expressible in elementary functions?

Why are "Most" integrals of elementary functions themselves not elementary functions?

When exactly must two elementary functions be identical if they are sufficiently close?

But is it really true that $\log(xy) = \log(x)+\log(y)$

Center of mass of a circular arc of radius R subtending an angle at the center

How can we show that $A(z,e^z)$ and $A(\ln (z),z)$ have no elementary inverse?

Equivalence between $f(x)e^g(x)$ being integrable and $r'(x) +g'(x)r(x)=f(x)$ having a function $r(x)$ that solves it.

What are the closed-form inverses of $x \sinh(x), x \cosh(x), x \tanh(x), x\ \text{sech}(x), x \coth(x), x\ \text{csch}(x)$?

Very trivial doubt on fractional exponents.

What are the closed-form inverses of $x+\sinh(x)$, $x+\cosh(x)$?

Calculating $\frac{1.01^5}{1.01^5-1}$ without calculator with good accuracy?

Given an arbitrary composite elementary function, does there exist some method to give us an intuition of its graph?

Trending Questions

Popular # Hahtags

Popular Questions