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 161 · Answer 1 · 2026-05-10 15:24:37

161

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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 10 May 2026 - 15:24

score 434 · Answer 2 · 2026-05-10 14:05:07

434

Views

Is division the same thing as a fraction?

Published on 10 May 2026 - 14:05

score 79 · Answer 3 · 2026-05-10 16:11:31

79

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

Published on 10 May 2026 - 16:11

score 129 · Answer 4 · 2026-05-10 19:56:54

129

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 10 May 2026 - 19:56

score 575 · Answer 5 · 2026-04-14 18:56:57

575

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

Published on 14 Apr 2026 - 18:56

score 36 · Answer 6 · 2026-04-10 15:26:32

36

Views

How to minus this fraction with different denominator?

Published on 10 Apr 2026 - 15:26

score 513 · Answer 7 · 2026-05-10 16:00:45

513

Views

Prove the tangent line exists

Published on 10 May 2026 - 16:00

score 59 · Answer 8 · 2026-04-09 00:02:45

59

Views

Fraction problem for primary school

Published on 09 Apr 2026 - 0:02

score 516 · Answer 9 · 2026-05-10 12:54:53

516

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

Published on 10 May 2026 - 12:54

score 77 · Answer 10 · 2026-05-10 20:17:24

77

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

Published on 10 May 2026 - 20:17

score 113 · Answer 11 · 2026-04-29 12:16:07

113

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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 29 Apr 2026 - 12:16

score 427 · Answer 12 · 2026-04-16 16:29:05

427

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

Published on 16 Apr 2026 - 16:29

score 203 · Answer 13 · 2026-05-10 20:43:56

203

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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 10 May 2026 - 20:43

score 57 · Answer 14 · 2026-04-15 13:27:25

57

Views

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

Published on 15 Apr 2026 - 13:27

score 178 · Answer 15 · 2026-05-10 16:13:02

178

Views

Fractional/rational form of $0.999...$

Published on 10 May 2026 - 16:13

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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