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

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

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

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

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

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

%C See A198866 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 negative: -0.97041584163559044784359265743084410...

%e positive: 0.676701594073077874194855720384016697...

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

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

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

%t r = x /.

%t FindRoot[f[x] == g[x], {x, -.98, -.97}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199078 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .67, .68}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199079 *)

%Y Cf. A198866.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 03 2011