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A201522
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Decimal expansion of greatest x satisfying 6*x^2 - 1 = sec(x) and 0 < x < Pi.
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3
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1, 4, 8, 9, 4, 8, 0, 6, 5, 6, 7, 3, 1, 8, 3, 3, 3, 2, 0, 3, 9, 9, 1, 2, 6, 0, 1, 7, 6, 7, 7, 3, 1, 7, 5, 4, 4, 9, 4, 3, 3, 6, 9, 1, 4, 8, 0, 6, 1, 5, 0, 7, 0, 4, 7, 3, 0, 5, 6, 8, 8, 5, 1, 9, 2, 7, 5, 0, 4, 5, 7, 7, 5, 1, 2, 6, 7, 8, 1, 6, 2, 9, 7, 4, 3, 0, 6, 2, 3, 7, 3, 9, 0, 3, 5, 3, 3, 5, 5
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OFFSET
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1,2
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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: 0.60805447799791305332799572251089761...
greatest: 1.489480656731833320399126017677317...
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MATHEMATICA
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a = 6; c = -1;
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, .6, .7}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, 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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