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A201406
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Decimal expansion of least x satisfying 2*x^2 = sec(x) and 0 < x < Pi.
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3
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8, 9, 2, 8, 7, 4, 3, 0, 6, 0, 5, 8, 9, 6, 1, 1, 2, 4, 4, 4, 7, 3, 7, 1, 9, 6, 9, 0, 1, 8, 6, 7, 7, 5, 1, 4, 6, 0, 1, 9, 5, 6, 8, 6, 1, 1, 9, 6, 7, 9, 4, 0, 3, 4, 0, 4, 7, 1, 7, 4, 5, 4, 5, 0, 3, 7, 8, 9, 5, 6, 9, 1, 0, 3, 2, 5, 6, 6, 5, 7, 7, 2, 1, 7, 1, 8, 2, 0, 4, 1, 5, 3, 4, 7, 5, 5, 1, 0, 7
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OFFSET
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0,1
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COMMENTS
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See A201397 for a guide to related sequences. The Mathematica program includes a graph.
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LINKS
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EXAMPLE
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least: 0.892874306058961124447371969018677514...
greatest: 1.2390826209275819187151092399019855...
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MATHEMATICA
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a = 2; c = 0;
f[x_] := a*x^2 + c; g[x_] := Sec[x]
Plot[{f[x], g[x]}, {x, 0, Pi/2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .8, 1}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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