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A198935 Decimal expansion of x>0 satisfying 3*x^2-3*cos(x)=4. 2

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

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

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

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

%N Decimal expansion of x>0 satisfying 3*x^2-3*cos(x)=4.

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

%e x=1.27477469729244956060192606401063809708471...

%t a = 3; b = -3; c = 4;

%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, 1.2, 1.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A198935 *)

%Y Cf. A198755.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 01 2011

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