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

%I #7 Feb 07 2025 16:44:05

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

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

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

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

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

%e x=1.9617279516465398416096274016767531700...

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

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

%t Plot[{f[x], g[x]}, {x, -.1, 2.3}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.96, 1.97}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198582 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 27 2011