Fungrim entry: 3fe47b

\operatorname{atan}\!\left(x\right) \ge \frac{\pi x}{\pi + 2 x}

Assumptions:

x \in \left[0, \infty\right)

TeX:

\operatorname{atan}\!\left(x\right) \ge \frac{\pi x}{\pi + 2 x}

x \in \left[0, \infty\right)

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}\!\left(z\right)$	Inverse tangent
`ConstPi`	$\pi$	The constant pi (3.14...)
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("3fe47b"),
    Formula(GreaterEqual(Atan(x), Div(Mul(ConstPi, x), Add(ConstPi, Mul(2, x))))),
    Variables(x),
    Assumptions(Element(x, ClosedOpenInterval(0, Infinity))))

Topics using this entry

Inverse tangent

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC