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A200003
Decimal expansion of greatest x satisfying 2*x^2 + cos(x) = 3*sin(x).
3
9, 8, 9, 4, 5, 0, 0, 1, 4, 4, 9, 3, 9, 4, 9, 1, 6, 7, 4, 8, 9, 7, 8, 8, 3, 3, 2, 6, 9, 5, 7, 1, 4, 9, 7, 5, 5, 4, 8, 1, 1, 9, 5, 4, 8, 4, 6, 2, 4, 1, 2, 6, 4, 4, 4, 2, 2, 0, 0, 1, 6, 0, 8, 4, 4, 9, 9, 6, 8, 2, 5, 8, 2, 7, 1, 5, 4, 1, 8, 2, 4, 3, 0, 4, 3, 1, 8, 3, 2, 4, 6, 9, 5, 2, 6, 3, 9, 1, 6
OFFSET
0,1
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: 0.45041223638324913376478190783839778...
greatest x: 0.989450014493949167489788332695714...
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, -.1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[r] (* A199967 *)
r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
RealDigits[r] (* A200003 *)
PROG
(PARI) a=2; b=1; c=3; solve(x=0.75, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018
CROSSREFS
Cf. A199949.
Sequence in context: A269222 A201994 A243277 * A159590 A309642 A146484
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 12 2011
STATUS
approved