A198360 - OEIS

%I #7 Aug 09 2021 07:44:20

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

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

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

%N Decimal expansion of greatest 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