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A199183
Decimal expansion of greatest x satisfying x^2 + 3*x*cos(x) = 1.
4
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
OFFSET
1,1
COMMENTS
See A199170 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
least: -1.3606727725137972152286027487379925...
greatest: 3.27746466341373058734587727791083...
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A005213 A075701 A016603 * A178908 A198552 A120633
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 04 2011
EXTENSIONS
a(92) onwards corrected by Georg Fischer, Aug 03 2021
STATUS
approved