Question

Prove the inequality $\frac{a}{1+a^2}+\frac{b}{1+b^2}+\frac{c}{1+c^2}\le\frac{3\sqrt3}{4}$

score 156 · Answer 1 · 2026-03-22 22:01:55

156

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Prove the inequality $\frac{a}{1+a^2}+\frac{b}{1+b^2}+\frac{c}{1+c^2}\le\frac{3\sqrt3}{4}$

Published on 22 Mar 2026 - 22:01

score 430 · Answer 2 · 2026-03-22 07:12:22

430

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Is division the same thing as a fraction?

Published on 22 Mar 2026 - 7:12

score 76 · Answer 3 · 2026-03-25 01:16:18

76

Views

Compute $\lim_{x \to +\infty}{\frac{\log(a+be^x)}{\sqrt{a+bx^2}}}$

Published on 25 Mar 2026 - 1:16

score 121 · Answer 4 · 2026-03-24 03:47:12

121

Views

Prove the inequality $\left(1+\frac{1}{a_1(1+a_1)}\right)...\left(1+\frac{1}{a_k(1+a_k)}\right)\ge\left(1+\frac{1}{p(1+p)}\right)^k$

Published on 24 Mar 2026 - 3:47

score 573 · Answer 5 · 2018-02-19 20:18:22

573

Views

Calculating $\lim_{x\to 0} \left[\frac{1}{\sin^2x}-\frac{1}{x^2}\right]$

Published on 19 Feb 2018 - 20:18

score 33 · Answer 6 · 2018-02-20 15:41:17

33

Views

How to minus this fraction with different denominator?

Published on 20 Feb 2018 - 15:41

score 508 · Answer 7 · 2026-03-25 03:00:44

508

Views

Prove the tangent line exists

Published on 25 Mar 2026 - 3:00

score 56 · Answer 8 · 2018-02-21 05:43:22

56

Views

Fraction problem for primary school

Published on 21 Feb 2018 - 5:43

score 512 · Answer 9 · 2026-03-25 01:18:07

512

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What is the value of $\sin^2 (\frac{\pi}{10}) \sin^2 (\frac{3\pi}{10})$?

Published on 25 Mar 2026 - 1:18

score 74 · Answer 10 · 2026-03-25 01:17:40

74

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the simpliest way of solving $\int\frac{\sqrt[4]{3x+5}}{x}\,\mathrm{d}x$?

Published on 25 Mar 2026 - 1:17

score 105 · Answer 11 · 2026-03-21 10:42:38

105

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Let $\sum\frac{1}{a^3+1}=2$. Prove that $\sum\frac{1-a}{a^2-a+1}\ge 0$

Published on 21 Mar 2026 - 10:42

score 424 · Answer 12 · 2018-02-23 18:05:43

424

Views

Simplifying $\left(\frac{1+\sin\theta + i \cos\theta}{1 + \sin\theta -i\cos \theta}\right)^n$

Published on 23 Feb 2018 - 18:05

score 200 · Answer 13 · 2026-03-25 03:03:19

200

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Compute the limit $\lim_{x\to 0} \frac{2^x+5^x-4^x-3^x}{5^x+4^x-3^x-2^x}$

Published on 25 Mar 2026 - 3:03

score 54 · Answer 14 · 2018-02-24 10:23:19

54

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Find all the complex numbers $z$ such that $w=\frac{2z-1}{z-2}$ has argument $\frac{\pi}2$

Published on 24 Feb 2018 - 10:23

score 171 · Answer 15 · 2026-03-25 06:03:23

171

Views

Fractional/rational form of $0.999...$

Published on 25 Mar 2026 - 6:03

List Question

Prove the inequality $\frac{a}{1+a^2}+\frac{b}{1+b^2}+\frac{c}{1+c^2}\le\frac{3\sqrt3}{4}$

Is division the same thing as a fraction?

Compute $\lim_{x \to +\infty}{\frac{\log(a+be^x)}{\sqrt{a+bx^2}}}$

Prove the inequality $\left(1+\frac{1}{a_1(1+a_1)}\right)...\left(1+\frac{1}{a_k(1+a_k)}\right)\ge\left(1+\frac{1}{p(1+p)}\right)^k$

Calculating $\lim_{x\to 0} \left[\frac{1}{\sin^2x}-\frac{1}{x^2}\right]$

How to minus this fraction with different denominator?

Prove the tangent line exists

Fraction problem for primary school

What is the value of $\sin^2 (\frac{\pi}{10}) \sin^2 (\frac{3\pi}{10})$?

the simpliest way of solving $\int\frac{\sqrt[4]{3x+5}}{x}\,\mathrm{d}x$?

Let $\sum\frac{1}{a^3+1}=2$. Prove that $\sum\frac{1-a}{a^2-a+1}\ge 0$

Simplifying $\left(\frac{1+\sin\theta + i \cos\theta}{1 + \sin\theta -i\cos \theta}\right)^n$

Compute the limit $\lim_{x\to 0} \frac{2^x+5^x-4^x-3^x}{5^x+4^x-3^x-2^x}$

Find all the complex numbers $z$ such that $w=\frac{2z-1}{z-2}$ has argument $\frac{\pi}2$

Fractional/rational form of $0.999...$

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