Fungrim entry: f5d28c

\operatorname{atan}(x) \le \frac{\pi}{2} \frac{x}{\sqrt{1 + {x}^{2}}}

Assumptions:

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

TeX:

\operatorname{atan}(x) \le \frac{\pi}{2} \frac{x}{\sqrt{1 + {x}^{2}}}

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

Definitions:

Fungrim symbol	Notation	Short description
`Atan`	$\operatorname{atan}(z)$	Inverse tangent
`Pi`	$\pi$	The constant pi (3.14...)
`Sqrt`	$\sqrt{z}$	Principal square root
`Pow`	${a}^{b}$	Power
`ClosedOpenInterval`	$\left[a, b\right)$	Closed-open interval
`Infinity`	$\infty$	Positive infinity

Source code for this entry:

Entry(ID("f5d28c"),
    Formula(LessEqual(Atan(x), Mul(Div(Pi, 2), Div(x, Sqrt(Add(1, Pow(x, 2))))))),
    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.

2021-03-15 19:12:00.328586 UTC