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Decimal expansion of x>0 satisfying x^2+3*x*sin(x)=1.
2

%I #11 Feb 07 2025 16:44:05

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

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

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

%N Decimal expansion of x>0 satisfying x^2+3*x*sin(x)=1.

%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 0.5081616569683919181277676293409924461...

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

%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, .50, .51}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199376 *)

%o (PARI) solve(x=0,1,x^2+3*x*sin(x)-1) \\ _Charles R Greathouse IV_, Dec 28 2011

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 05 2011