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A200012
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Decimal expansion of least x satisfying x^2 - cos(x) = 2*sin(x) (negated).
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3
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3, 9, 4, 1, 2, 4, 1, 9, 2, 8, 5, 8, 9, 7, 5, 9, 6, 0, 0, 9, 9, 7, 0, 5, 3, 9, 9, 3, 5, 4, 5, 9, 0, 0, 9, 8, 5, 3, 6, 9, 2, 2, 4, 9, 6, 1, 9, 3, 9, 1, 2, 2, 9, 7, 9, 2, 1, 9, 8, 4, 8, 1, 1, 6, 8, 5, 3, 1, 1, 8, 7, 4, 1, 7, 6, 0, 2, 4, 8, 1, 7, 9, 3, 5, 8, 3, 4, 5, 6, 0, 3, 0, 7, 1, 7, 9, 2, 1, 5
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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: -0.3941241928589759600997053993545900...
greatest x: 1.450938449634974431128285576690357738...
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MATHEMATICA
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a = 1; b = -1; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.4, -.3}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
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PROG
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(PARI) a=1; b=-1; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 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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