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Fungrim entry: f5d28c

atan(x)π2x1+x2\operatorname{atan}(x) \le \frac{\pi}{2} \frac{x}{\sqrt{1 + {x}^{2}}}
Assumptions:x[0,)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
Atanatan(z)\operatorname{atan}(z) Inverse tangent
Piπ\pi The constant pi (3.14...)
Sqrtz\sqrt{z} Principal square root
Powab{a}^{b} Power
ClosedOpenInterval[a,b)\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))))

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

2020-01-31 18:09:28.494564 UTC