A199187 - OEIS

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

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

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

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

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

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

%e negative: -1.6364435519550414220675930311871282455...

%e positive:  3.56968633396230393049792896687800143343...

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

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -1.7, -1.6}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199186 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 3.56, 3.57}, WorkingPrecision -> 110]

%t RealDigits[r]  (*  A199187 *)

%Y Cf. A199170.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Nov 04 2011