A199271 - OEIS

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

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

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

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

%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 1,2

%A _Clark Kimberling_, Nov 04 2011