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

%I #6 Feb 07 2025 16:44:05

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

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

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

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

%C See A198414 for a guide to related sequences. The Mathematica program includes a graph.

%e x=2.597659611167348352719860846931783600...

%t a = 1; b = -2; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -.2, 3}]

%t r = x /. FindRoot[f[x] == g[x], {x, 2.59, 2.60}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198429 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Oct 25 2011