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A200111
Decimal expansion of least x satisfying 2*x^2-cos(x)=3*sin(x).
4
2, 7, 4, 1, 8, 5, 9, 2, 8, 0, 5, 9, 8, 3, 1, 5, 7, 9, 0, 1, 2, 9, 3, 8, 5, 7, 6, 1, 6, 5, 9, 2, 6, 1, 0, 6, 7, 1, 9, 3, 4, 6, 4, 4, 2, 6, 5, 9, 6, 6, 3, 7, 1, 8, 4, 8, 3, 7, 3, 1, 3, 2, 8, 7, 6, 3, 4, 5, 8, 4, 4, 1, 6, 6, 5, 1, 5, 9, 0, 3, 6, 8, 1, 0, 1, 8, 6, 6, 3, 2, 2, 3, 7, 2, 6, 9, 8, 8, 1
OFFSET
0,1
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.2741859280598315790129385761659261067...
greatest x: 1.25741142949475925602237309814803895...
MATHEMATICA
a = 2; b = -1; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.28, -.27}, WorkingPrecision -> 110]
RealDigits[r] (* A200111 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.25, 1.26}, WorkingPrecision -> 110]
RealDigits[r] (* A200112 *)
PROG
(PARI) a=2; b=-1; c=3; solve(x=-.28, -.27, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 22 2018
CROSSREFS
Cf. A199949.
Sequence in context: A353908 A144805 A198745 * A201747 A117233 A051559
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 13 2011
STATUS
approved