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

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

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

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

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

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

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

%e x=1.96839750785873284138289918460169624078672...

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

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

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

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

%t RealDigits[r] (* A198567 *)

%Y Cf. A198414.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 27 2011