A199786 - OEIS

%I #5 Mar 30 2012 18:57:58

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

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

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

%N Decimal expansion of x>0 satisfying 3*x^2-4*x*cos(x)=sin(x).

%C See A199597 for a guide to related sequences.  The Mathematica program includes a graph.

%e x=1.000401978886349072576800182201212279659791...

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

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

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

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

%t RealDigits[r]    (* A199786 *)

%Y Cf. A199597.

%K nonn,cons

%O 1,5

%A _Clark Kimberling_, Nov 10 2011