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A199964
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Decimal expansion of greatest x satisfying x^2 + 4*cos(x) = 3*sin(x).
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3
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2, 1, 7, 8, 8, 4, 3, 3, 0, 3, 0, 3, 8, 4, 3, 8, 4, 7, 8, 7, 4, 7, 3, 5, 1, 5, 4, 6, 6, 3, 1, 1, 2, 0, 7, 8, 8, 0, 9, 8, 3, 8, 5, 5, 8, 5, 8, 9, 3, 8, 0, 7, 1, 9, 4, 3, 7, 4, 9, 0, 8, 7, 6, 0, 0, 4, 7, 5, 6, 4, 2, 6, 7, 4, 4, 8, 5, 4, 0, 4, 7, 5, 3, 2, 0, 2, 9, 5, 4, 4, 4, 8, 4, 5, 2, 5, 9, 8, 6
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OFFSET
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1,1
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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: 1.2397511548307033226630942987091820...
greatest x: 2.17884330303843847874735154663112...
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MATHEMATICA
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a = 1; b = 4; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.23, 1.24}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 2.17, 2.18}, WorkingPrecision -> 110]
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PROG
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(PARI) a=1; b=4; c=3; solve(x=2, 3, 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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