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A200308
Decimal expansion of greatest x satisfying 4*x^2 - 4*cos(x) = 3*sin(x).
3
1, 0, 6, 7, 4, 0, 8, 4, 8, 5, 6, 9, 3, 5, 9, 1, 7, 2, 3, 8, 3, 9, 2, 6, 0, 5, 6, 7, 0, 0, 7, 0, 6, 4, 1, 8, 4, 7, 6, 0, 4, 6, 0, 0, 3, 5, 9, 5, 3, 0, 2, 7, 8, 6, 5, 0, 5, 4, 6, 5, 9, 3, 0, 4, 0, 8, 3, 5, 4, 3, 1, 7, 8, 2, 0, 4, 4, 8, 3, 7, 9, 5, 5, 4, 1, 5, 1, 6, 5, 4, 8, 3, 2, 1, 1, 0, 8, 1, 9
OFFSET
1,3
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.6174065144201321316882984350723098...
greatest x: 1.06740848569359172383926056700706...
MATHEMATICA
a = 4; b = -4; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.62, -.63}, WorkingPrecision -> 110]
RealDigits[r] (* A200307 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r] (* A200308 *)
PROG
(PARI) a=4; b=-4; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 10 2018
CROSSREFS
Cf. A199949.
Sequence in context: A144028 A089321 A299629 * A097410 A367312 A195792
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 16 2011
STATUS
approved