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A199962
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Decimal expansion of greatest x satisfying x^2 + 3*cos(x) = 4*sin(x).
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3
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2, 2, 3, 5, 8, 0, 9, 2, 8, 2, 0, 6, 4, 5, 6, 9, 1, 2, 1, 1, 1, 5, 2, 6, 4, 1, 4, 8, 3, 1, 7, 0, 1, 9, 8, 4, 4, 2, 4, 8, 0, 4, 9, 2, 0, 3, 9, 2, 6, 5, 3, 9, 0, 4, 0, 4, 3, 4, 1, 5, 0, 9, 1, 3, 0, 2, 6, 0, 5, 2, 4, 8, 0, 6, 1, 5, 1, 6, 5, 3, 9, 7, 5, 3, 5, 0, 8, 8, 3, 7, 8, 7, 4, 1, 9, 3, 2, 6, 9
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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: 0.7589622035176968518571982860561050925949...
greatest x: 2.23580928206456912111526414831701984424...
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MATHEMATICA
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a = 1; b = 3; c = 4;
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, .75, .76}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 2.2, 2.3}, WorkingPrecision -> 110]
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PROG
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(PARI) a=1; b=3; c=4; 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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