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A200108
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Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = sin(x).
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3
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8, 4, 0, 2, 6, 3, 5, 1, 7, 7, 1, 5, 7, 6, 7, 8, 9, 9, 3, 4, 7, 9, 7, 3, 4, 9, 9, 6, 4, 8, 3, 5, 5, 7, 9, 7, 3, 6, 5, 0, 2, 5, 3, 9, 0, 5, 3, 5, 1, 5, 2, 6, 6, 1, 1, 7, 3, 5, 4, 3, 6, 3, 9, 2, 5, 1, 7, 4, 5, 5, 5, 6, 5, 3, 6, 2, 5, 0, 2, 1, 5, 6, 7, 8, 0, 3, 5, 1, 8, 3, 7, 2, 4, 6, 3, 0, 2, 7, 7
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OFFSET
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0,1
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COMMENTS
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See A199949 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 x: -0.4690323711198093057335493058025105005500...
greatest x: 0.840263517715767899347973499648355797365...
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MATHEMATICA
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a = 2; b = -1; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /.
FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
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PROG
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(PARI) a=2; b=-1; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018
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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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