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A199183
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Decimal expansion of greatest x satisfying x^2 + 3*x*cos(x) = 1.
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4
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3, 2, 7, 7, 4, 6, 4, 6, 6, 3, 4, 1, 3, 7, 3, 0, 5, 8, 7, 3, 4, 5, 8, 7, 7, 2, 7, 7, 9, 1, 0, 8, 3, 5, 7, 1, 7, 7, 4, 7, 8, 5, 8, 8, 5, 4, 4, 7, 9, 5, 3, 1, 4, 9, 0, 1, 3, 4, 2, 1, 2, 3, 2, 8, 6, 6, 2, 2, 6, 8, 2, 3, 3, 2, 8, 8, 5, 6, 8, 8, 0, 4, 7, 6, 8, 9, 7, 7, 7, 9, 5, 6, 8, 9, 7, 5, 7, 0, 0
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OFFSET
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1,1
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COMMENTS
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See A199170 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: -1.3606727725137972152286027487379925...
greatest: 3.27746466341373058734587727791083...
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MATHEMATICA
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a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
RealDigits[r] (* A199182 least of four roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.27, 3.28}, WorkingPrecision -> 110]
RealDigits[r] (* A199183 greatest of four roots *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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