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A198934 Decimal expansion of x>0 satisfying 3*x^2-3*cos(x)=2. 2

%I #5 Mar 30 2012 18:57:56

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

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

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

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

%C See A198755 for a guide to related sequences. The Mathematica program includes a graph.

%e x=1.0706265440208273230931192923651719814606561...

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

%t f[x_] := a*x^2 + b*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, 1.07, 1.08}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198934 *)

%Y Cf. A198755.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 01 2011

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