login
A200116
Decimal expansion of least x satisfying 2*x^2 - 2*cos(x) = sin(x), negated.
3
6, 8, 0, 3, 2, 6, 4, 1, 4, 1, 3, 8, 6, 7, 9, 2, 9, 6, 2, 3, 9, 6, 3, 1, 6, 2, 0, 7, 3, 6, 4, 1, 9, 1, 7, 6, 8, 6, 5, 5, 3, 0, 2, 5, 8, 0, 2, 1, 0, 8, 1, 4, 5, 3, 5, 6, 0, 8, 0, 7, 7, 9, 5, 9, 8, 9, 2, 6, 3, 3, 9, 2, 2, 7, 0, 8, 1, 5, 4, 8, 2, 0, 3, 7, 7, 9, 1, 0, 0, 2, 2, 0, 1, 2, 5, 7, 6, 4, 7
OFFSET
0,1
COMMENTS
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
LINKS
EXAMPLE
least x: -0.680326414138679296239631620736419...
greatest x: 0.9847126993630673524991380090748...
MATHEMATICA
a = 2; b = -2; c = 1;
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, -.69, -.68}, WorkingPrecision -> 110]
RealDigits[r] (* A200116 *)
r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]
RealDigits[r] (* A200117 *)
PROG
(PARI) a=2; b=-2; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 29 2018
CROSSREFS
Cf. A199949.
Sequence in context: A011315 A268508 A021151 * A360500 A308314 A097909
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Nov 14 2011
STATUS
approved