|
%I #5 Mar 30 2012 18:57:54
%S 9,5,4,3,4,7,7,7,6,6,0,8,7,5,5,6,7,2,1,2,0,9,0,0,9,5,4,7,9,3,3,9,1,3,
%T 7,3,2,9,4,4,2,8,2,7,1,3,8,3,6,2,0,7,0,8,3,5,8,2,4,7,6,5,0,6,4,0,9,9,
%U 8,5,6,9,4,5,8,2,9,1,3,1,7,6,9,1,7,4,3,5,0,6,3,4,2,2,2,0,1,6,6
%N Decimal expansion of least x having 4*x^2+2x=3*cos(x).
%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.
%e least x: -0.95434777660875567212090095479339137329...
%e greatest x: 0.58045712444593316179721965142881907589...
%t a = 4; b = 2; c = 3;
%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]
%t Plot[{f[x], g[x]}, {x, -1, 1}]
%t r1 = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t RealDigits[r1] (* A198359 *)
%t r2 = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
%t RealDigits[r2] (* A198360 *)
%Y Cf. A197737.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Oct 24 2011
|
