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A200115
Decimal expansion of greatest x satisfying 2*x^2 - cos(x) = 4*sin(x).
3
1, 4, 3, 1, 7, 7, 8, 7, 3, 2, 6, 8, 7, 2, 3, 1, 1, 3, 1, 8, 2, 0, 5, 9, 1, 7, 9, 9, 7, 0, 0, 5, 5, 8, 8, 4, 3, 9, 2, 4, 1, 9, 0, 4, 9, 6, 6, 1, 7, 0, 4, 2, 0, 0, 6, 6, 7, 9, 9, 9, 3, 2, 1, 8, 9, 6, 2, 3, 2, 9, 2, 4, 0, 8, 7, 8, 6, 0, 2, 1, 8, 6, 9, 6, 7, 5, 3, 0, 7, 9, 3, 7, 2, 9, 1, 1, 5, 0, 1
OFFSET
1,2
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.22123471685655084592875161456517915661...
greatest x: 1.431778732687231131820591799700558843...
MATHEMATICA
a = 2; b = -1; c = 4;
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, -.23, -.22}, WorkingPrecision -> 110]
RealDigits[r] (* A200114 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.43, 1.44}, WorkingPrecision -> 110]
RealDigits[r] (* A200115 *)
PROG
(PARI) a=2; b=-1; c=4; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018
CROSSREFS
Cf. A199949.
Sequence in context: A103552 A127673 A016698 * A332496 A038763 A200384
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 13 2011
STATUS
approved