Elementary Functions - 4.32 Inequalities
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 4.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3}}
\cosh@@{x} \leq \left(\frac{\sinh@@{x}}{x}\right)^{3} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(x) <= ((sinh(x))/(x))^(3)
|
Cosh[x] <= (Divide[Sinh[x],x])^(3)
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{x}\cos@@{x} < \tanh@@{x}}
\sin@@{x}\cos@@{x} < \tanh@@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0} | sin(x)*cos(x) < tanh(x)
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Sin[x]*Cos[x] < Tanh[x]
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Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.32.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{x} < x}
\tanh@@{x} < x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0} | tanh(x) < x
|
Tanh[x] < x
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}}}
|\cosh@@{x}-\cosh@@{y}| \geq |x-y|\sqrt{\sinh@@{x}\sinh@@{y}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x > 0, y > 0} | abs(cosh(x)- cosh(y)) >= abs(x - y)*sqrt(sinh(x)*sinh(y))
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Abs[Cosh[x]- Cosh[y]] >= Abs[x - y]*Sqrt[Sinh[x]*Sinh[y]]
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Failure | Failure | Successful [Tested: 9] | Successful [Tested: 9] |
| 4.32.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x}}
\atan@@{x} \leq \tfrac{1}{2}\pi\tanh@@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \geq 0} | arctan(x) <= (1)/(2)*Pi*tanh(x)
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ArcTan[x] <= Divide[1,2]*Pi*Tanh[x]
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Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |