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Fungrim entry: b0a4e9

atan ⁣(x)x1+x2\operatorname{atan}\!\left(x\right) \ge \frac{x}{\sqrt{1 + {x}^{2}}}
Assumptions:x[0,)x \in \left[0, \infty\right)
TeX:
\operatorname{atan}\!\left(x\right) \ge \frac{x}{\sqrt{1 + {x}^{2}}}

x \in \left[0, \infty\right)
Definitions:
Fungrim symbol Notation Short description
Atanatan ⁣(z)\operatorname{atan}\!\left(z\right) Inverse tangent
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("b0a4e9"),
    Formula(GreaterEqual(Atan(x), Div(x, Sqrt(Add(1, Pow(x, 2)))))),
    Variables(x),
    Assumptions(Element(x, ClosedOpenInterval(0, Infinity))))

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2019-09-19 20:12:49.583742 UTC