|
%I #5 Mar 30 2012 18:57:57
%S 2,1,7,0,8,5,3,3,9,9,9,4,4,2,6,8,4,6,6,1,8,2,9,6,7,7,8,9,6,2,4,5,3,8,
%T 9,9,3,1,8,7,7,3,3,2,7,6,9,0,3,4,8,5,9,1,8,0,8,0,1,0,9,5,9,7,0,0,1,5,
%U 1,5,5,8,6,4,8,0,9,7,7,9,1,2,2,0,6,3,3,3,8,1,2,6,1,1,7,3,3,6,7
%N Decimal expansion of greatest x satisfying x^2-2*x*sin(x)=-2*cos(x).
%C See A199370 for a guide to related sequences. The Mathematica program includes a graph.
%e x=2.17085339994426846618296778962453899318773...
%t a = 1; b = -2; c = -2;
%t f[x_] := a*x^2 + b*x*Sin[x]; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -Pi, Pi}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, 2.17, 2.18}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199458 greatest root *)
%Y Cf. A199429.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Nov 06 2011
|
