Elementary Functions - 4.18 Inequalities
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 4.18.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2x}{\pi} \leq \sin@@{x}}
\frac{2x}{\pi} \leq \sin@@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq x, x \leq \frac{1}{2}\pi} | (2*x)/(Pi) <= sin(x)
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Divide[2*x,Pi] <= Sin[x]
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Failure | Failure | Successful [Tested: 2] | Successful [Tested: 2] |
| 4.18.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{x} \leq x}
\sin@@{x} \leq x |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq x, x \leq \frac{1}{2}\pi} | sin(x) <= x
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Sin[x] <= x
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Failure | Failure | Successful [Tested: 2] | Successful [Tested: 2] |
| 4.18.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x \leq \tan@@{x}}
x \leq \tan@@{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq x, x < \frac{1}{2}\pi} | x <= tan(x)
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x <= Tan[x]
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Failure | Failure | Successful [Tested: 2] | Successful [Tested: 2] |
| 4.18.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{x} \leq \frac{\sin@@{x}}{x}}
\cos@@{x} \leq \frac{\sin@@{x}}{x} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq x, x \leq \pi} | cos(x) <= (sin(x))/(x)
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Cos[x] <= Divide[Sin[x],x]
|
Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.18.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@@{x}}{x} \leq 1}
\frac{\sin@@{x}}{x} \leq 1 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq x, x \leq \pi} | (sin(x))/(x) <= 1
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Divide[Sin[x],x] <= 1
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Failure | Failure | Successful [Tested: 3] | Successful [Tested: 3] |
| 4.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pi < \frac{\sin@{\pi x}}{x(1-x)}}
\pi < \frac{\sin@{\pi x}}{x(1-x)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < x, x < 1} | Pi < (sin(Pi*x))/(x*(1 - x))
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Pi < Divide[Sin[Pi*x],x*(1 - x)]
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Failure | Failure | Successful [Tested: 1] | Successful [Tested: 1] |
| 4.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\sin@{\pi x}}{x(1-x)} \leq 4}
\frac{\sin@{\pi x}}{x(1-x)} \leq 4 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < x, x < 1} | (sin(Pi*x))/(x*(1 - x)) <= 4
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Divide[Sin[Pi*x],x*(1 - x)] <= 4
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Failure | Failure | Successful [Tested: 1] | Successful [Tested: 1] |
| 4.18.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sinh@@{y}| \leq |\sin@@{z}|\leq\cosh@@{y}}
|\sinh@@{y}| \leq |\sin@@{z}|\leq\cosh@@{y} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(sinh(y)) <= abs(sin(x + y*I)) <= cosh(y)
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Abs[Sinh[y]] <= Abs[Sin[x + y*I]] <= Cosh[y]
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Failure | Failure | Error | Successful [Tested: 18] |
| 4.18.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sinh@@{y}| \leq |\cos@@{z}|\leq\cosh@@{y}}
|\sinh@@{y}| \leq |\cos@@{z}|\leq\cosh@@{y} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(sinh(y)) <= abs(cos(x + y*I)) <= cosh(y)
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Abs[Sinh[y]] <= Abs[Cos[x + y*I]] <= Cosh[y]
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Failure | Failure | Error | Successful [Tested: 18] |
| 4.18.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\csc@@{z}| \leq \csch@@{|y|}}
|\csc@@{z}| \leq \csch@@{|y|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(csc(x + y*I)) <= csch(abs(y))
|
Abs[Csc[x + y*I]] <= Csch[Abs[y]]
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Failure | Failure | Successful [Tested: 18] | Successful [Tested: 18] |
| 4.18.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cos@@{z}| \leq \cosh@@{|z|}}
|\cos@@{z}| \leq \cosh@@{|z|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(cos(z)) <= cosh(abs(z))
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Abs[Cos[z]] <= Cosh[Abs[z]]
|
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 4.18.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sin@@{z}| \leq \sinh@@{|z|}}
|\sin@@{z}| \leq \sinh@@{|z|} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(sin(z)) <= sinh(abs(z))
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Abs[Sin[z]] <= Sinh[Abs[z]]
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Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 4.18#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\cos@@{z}| < 2}
|\cos@@{z}| < 2 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | abs(cos(z)) < 2
|
Abs[Cos[z]] < 2
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Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
| 4.18#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\sin@@{z}| \leq \tfrac{6}{5}|z|}
|\sin@@{z}| \leq \tfrac{6}{5}|z| |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z| < 1} | abs(sin(z)) <= (6)/(5)*abs(z)
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Abs[Sin[z]] <= Divide[6,5]*Abs[z]
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Failure | Failure | Successful [Tested: 1] | Successful [Tested: 1] |