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

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

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

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

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

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

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

%e x=1.0817900512851302473726818478054114590342026...

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

%t f[x_] := a*x^2 + b*x*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, 1.08, 1.09}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199872 *)

%Y Cf. A199597.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 11 2011