A199272 - OEIS

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

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

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

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

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

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

%e negative: -1.342905122329356157795629258382825825170...

%e positive:  0.976312273615130123076470141335091567967...

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

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -1.35, -1.34}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A199271 *)

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

%t RealDigits[r]   (* A199272 *)

%Y Cf. A199170.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 04 2011