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A199286 Decimal expansion of x>0 satisfying 3*x^2+2*x*cos(x)=1. 3

%I #5 Mar 30 2012 18:57:57

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

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

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

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

%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.

%e negative: -0.840914700055474492704399020053615852...

%e positive: 0.3432728196270004264786970275097026953...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -.85, -.84}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199285 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .34, .35}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199286 *)

%Y Cf. A199170.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 05 2011

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)