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

%I #8 Feb 07 2025 16:44:05

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

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

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

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

%C See A199370 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 1.065503773536329223691143404854425625668...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, 1.06, 1.07}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199375 *)

%Y Cf. A199370.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 05 2011