Question

Evaluating $\lim_{x\to+\infty}\frac{(\sqrt{x+x^3}-x)\ln(\frac{\sqrt{4x+1}}{2\sqrt x +3})}{x\arctan x}$

score 91 · Answer 1 · 2019-01-14 16:36:33

91

Views

Evaluating $\lim_{x\to+\infty}\frac{(\sqrt{x+x^3}-x)\ln(\frac{\sqrt{4x+1}}{2\sqrt x +3})}{x\arctan x}$

Published on 14 Jan 2019 - 16:36

score 312 · Answer 2 · 2019-01-15 12:06:15

312

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If $\sqrt x + \sqrt y + \sqrt z = \sqrt a + \sqrt b + \sqrt c$ is there a polynomial P such that $P(x, y, z, a, b, c) = 0$?

Published on 15 Jan 2019 - 12:06

score 209 · Answer 3 · 2026-03-25 09:23:27

209

Views

Solving $\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$

Published on 25 Mar 2026 - 9:23

score 89 · Answer 4 · 2026-03-26 07:53:55

89

Views

Prove the equality $[\sqrt n+\sqrt{n+1}]=[\sqrt{4n+2}]$.

Published on 26 Mar 2026 - 7:53

score 216 · Answer 5 · 2026-03-25 13:59:46

216

Views

Expressing, in terms of real radicals, the trigonometric functions generated by cubic equations with integer coefficients

Published on 25 Mar 2026 - 13:59

score 40 · Answer 6 · 2019-01-20 12:03:37

40

Views

Let $a;b;c\in R+$ such that $a+\frac{b}{16}+\frac{c}{81}\le \:3;\frac{b}{16}+\frac{c}{81}\le 2;c\le 81$. Find maxima of $A$

Published on 20 Jan 2019 - 12:03

score 41 · Answer 7 · 2026-03-24 20:36:53

41

Views

Inequality with square roots where solution found with discriminant is not valid

Published on 24 Mar 2026 - 20:36

score 73 · Answer 8 · 2019-01-21 13:37:32

73

Views

Fifth root of $x$ raised to three...

Published on 21 Jan 2019 - 13:37

score 125 · Answer 9 · 2019-01-21 13:47:40

125

Views

What method of finding the square root they use in this screenshot?

Published on 21 Jan 2019 - 13:47

score 128 · Answer 10 · 2019-01-22 01:32:30

128

Views

Different ways to express $\sqrt{a}+\sqrt{b}$

Published on 22 Jan 2019 - 1:32

score 75 · Answer 11 · 2019-01-23 18:37:41

75

Views

Simplifying a solution to $x^2 = 4 + 2\sqrt{2}$

Published on 23 Jan 2019 - 18:37

score 548 · Answer 12 · 2026-03-25 09:33:46

548

Views

Algorithm for regular continued fraction of a square root

Published on 25 Mar 2026 - 9:33

score 216 · Answer 13 · 2026-03-25 07:44:55

216

Views

Inequality. ${{\sqrt{a}+\sqrt{b}+\sqrt{c}} \over {2}} \ge {{1} \over {\sqrt{a}}} + {{1} \over {\sqrt{b}}} + {{1} \over {\sqrt{c}}}$

Published on 25 Mar 2026 - 7:44

score 134 · Answer 14 · 2019-01-25 06:53:20

134

Views

prove the inequality $\left({1-x\over1+x}\right)^{1/2}\lt{\ln(1+x)\over \arcsin(x)}\lt1$ for $x\in (0,1)$

Published on 25 Jan 2019 - 6:53

score 104 · Answer 15 · 2019-01-26 07:33:54

104

Views

If x,y and z are positive integers and $\frac 1x + \frac 1y = \frac 1z$ then $\sqrt{x^2+y^2+z^2}$ is rational.

Published on 26 Jan 2019 - 7:33

List Question

Evaluating $\lim_{x\to+\infty}\frac{(\sqrt{x+x^3}-x)\ln(\frac{\sqrt{4x+1}}{2\sqrt x +3})}{x\arctan x}$

If $\sqrt x + \sqrt y + \sqrt z = \sqrt a + \sqrt b + \sqrt c$ is there a polynomial P such that $P(x, y, z, a, b, c) = 0$?

Solving $\sqrt{1+\sqrt{2+\sqrt{3+\ldots}}}$

Prove the equality $[\sqrt n+\sqrt{n+1}]=[\sqrt{4n+2}]$.

Expressing, in terms of real radicals, the trigonometric functions generated by cubic equations with integer coefficients

Let $a;b;c\in R+$ such that $a+\frac{b}{16}+\frac{c}{81}\le \:3;\frac{b}{16}+\frac{c}{81}\le 2;c\le 81$. Find maxima of $A$

Inequality with square roots where solution found with discriminant is not valid

Fifth root of $x$ raised to three...

What method of finding the square root they use in this screenshot?

Different ways to express $\sqrt{a}+\sqrt{b}$

Simplifying a solution to $x^2 = 4 + 2\sqrt{2}$

Algorithm for regular continued fraction of a square root

Inequality. ${{\sqrt{a}+\sqrt{b}+\sqrt{c}} \over {2}} \ge {{1} \over {\sqrt{a}}} + {{1} \over {\sqrt{b}}} + {{1} \over {\sqrt{c}}}$

prove the inequality $\left({1-x\over1+x}\right)^{1/2}\lt{\ln(1+x)\over \arcsin(x)}\lt1$ for $x\in (0,1)$

If x,y and z are positive integers and $\frac 1x + \frac 1y = \frac 1z$ then $\sqrt{x^2+y^2+z^2}$ is rational.

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