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A199616
Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=2*sin(x).
3
3, 5, 1, 5, 6, 1, 3, 1, 9, 9, 6, 8, 7, 3, 5, 8, 0, 2, 3, 8, 4, 2, 1, 8, 0, 2, 1, 0, 7, 0, 4, 0, 3, 0, 7, 9, 2, 2, 1, 7, 8, 8, 8, 8, 6, 7, 9, 8, 1, 9, 3, 3, 5, 0, 7, 3, 8, 3, 3, 3, 5, 6, 9, 7, 8, 4, 4, 2, 4, 3, 4, 5, 9, 1, 6, 5, 7, 2, 6, 4, 8, 5, 7, 2, 3, 9, 2, 0, 0, 0, 7, 5, 7, 6, 0, 2, 3, 4, 1
OFFSET
1,1
COMMENTS
See A199597 for a guide to related sequences. The Mathematica program includes a graph.
EXAMPLE
least: -0.856374049744346109322078062564729199476600...
greatest: 3.515613199687358023842180210704030792217...
MATHEMATICA
a = 1; b = 4; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 4}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.86, -.85}, WorkingPrecision -> 110]
RealDigits[r] (* A199615, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision -> 110]
RealDigits[r] (* A199616, greatest of 4 roots *)
CROSSREFS
Cf. A199597.
Sequence in context: A256598 A155526 A076553 * A173973 A344076 A333336
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 08 2011
STATUS
approved