A200123 - OEIS

%I #8 Jun 30 2018 07:06:46

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

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

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

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

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

%H G. C. Greubel, <a href="/A200123/b200123.txt">Table of n, a(n) for n = 1..10000</a>

%e least x: -0.70415945703712255268105833349948348210...

%e greatest x: 1.210301102156057859192844246759434780...

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

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -.71, -.70}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200122 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.2, 1.3}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A200123 *)

%o (PARI) a=2; b=-3; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 29 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 14 2011