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A200286
Decimal expansion of least x satisfying 4*x^2 - cos(x) = sin(x).
3
5, 8, 8, 8, 5, 1, 7, 4, 2, 6, 7, 5, 0, 4, 1, 1, 7, 9, 9, 9, 9, 6, 5, 9, 7, 1, 4, 6, 4, 4, 8, 4, 8, 0, 3, 8, 1, 8, 0, 1, 6, 1, 3, 7, 1, 7, 0, 6, 1, 7, 3, 1, 0, 3, 1, 5, 9, 4, 8, 7, 4, 1, 6, 6, 3, 8, 7, 9, 2, 3, 6, 2, 6, 0, 5, 0, 4, 2, 8, 3, 7, 4, 8, 0, 4, 0, 8, 0, 9, 8, 6, 0, 4, 9, 9, 8, 2, 2, 7
OFFSET
0,1
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.37540364996113984869295773583715442...
greatest x: 0.588851742675041179999659714644848...
MATHEMATICA
a = 4; b = -1; c = 1;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.38, -.37}, WorkingPrecision -> 110]
RealDigits[r] (* A200285 *)
r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
RealDigits[r] (* A200286 *)
PROG
(PARI) a=4; b=-1; c=1; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 07 2018
CROSSREFS
Cf. A199949.
Sequence in context: A247037 A265274 A365523 * A073822 A198606 A031165
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 15 2011
STATUS
approved