A200278 - OEIS

%I #12 Jul 06 2018 03:03:48

%S 1,0,0,0,3,0,3,6,3,9,2,8,3,5,9,0,1,8,5,1,8,7,2,2,5,0,3,5,7,4,4,1,8,0,

%T 0,1,2,2,5,8,5,6,5,6,1,8,5,2,9,2,0,2,6,4,2,6,3,2,2,5,7,4,9,5,4,6,0,9,

%U 3,0,3,2,3,5,9,3,8,1,8,7,9,0,3,9,0,6,4,2,4,1,8,6,9,7,4,6,3,5,4

%N Decimal expansion of greatest x satisfying 3*x^2 - 4*cos(x) = sin(x).

%C See A199949 for a guide to related sequences.  The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200278/b200278.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.81771521879230454511191454208365777...

%e greatest x: 1.000303639283590185187225035744180...

%t a = 3; b = -4; c = 1;

%t f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]

%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /.  FindRoot[f[x] == g[x], {x, -.82, -.81}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200277  *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200278 *)

%o (PARI) a=3; b=-4; c=1; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,5

%A _Clark Kimberling_, Nov 15 2011