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Fungrim entry: d04a5b

atan ⁣(x)π2tanh ⁣(x)\operatorname{atan}\!\left(x\right) \le \frac{\pi}{2} \tanh\!\left(x\right)
Assumptions:x[0,)x \in \left[0, \infty\right)
TeX:
\operatorname{atan}\!\left(x\right) \le \frac{\pi}{2} \tanh\!\left(x\right)

x \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
ConstPiπ\pi The constant pi (3.14...)
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Source code for this entry:
Entry(ID("d04a5b"),
    Formula(LessEqual(Atan(x), Mul(Div(ConstPi, 2), Tanh(x)))),
    Variables(x),
    Assumptions(Element(x, ClosedOpenInterval(0, Infinity))))

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2019-06-18 07:49:59.356594 UTC