A199777 - OEIS

%I #8 Feb 08 2025 22:32:44

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

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

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

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

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

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e 1.48054633175491203776764305792327587329853...

%t a = 2; b = -3; c = 4;

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

%t Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.48, 1.49}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199777 *)

%Y Cf. A199597.

%K nonn,cons,changed

%O 1,2

%A _Clark Kimberling_, Nov 10 2011