A200234 - OEIS

%I #8 Jul 01 2018 13:57:29

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

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

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

%N Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = 3*sin(x).

%C See A199949 for a guide to related sequences.  The Mathematica program includes a graph.

%H G. C. Greubel, <a href="/A200234/b200234.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.432052760425723131996383607455372280...

%e greatest x: 1.0929613126196942696433829125566221...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -.44, -.43}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200233 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.08, 1.09}, WorkingPrecision -> 110]

%t RealDigits[r]   (* A200234 *)

%o (PARI) a=3; b=-2; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 30 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, Nov 14 2011