A199954 - OEIS

%I #10 Jun 22 2018 23:08:50

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

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

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

%N Decimal expansion of greatest x satisfying x^2+cos(x)=4*sin(x).

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

%H G. C. Greubel, <a href="/A199954/b199954.txt">Table of n, a(n) for n = 1..10000</a>

%e least x:  0.26157393647481130212296420178312116039782...

%e greatest x: 2.011137342229330846002506540879639388630...

%t a = 1; b = 1; c = 4;

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

%t Plot[{f[x], g[x]}, {x, -1, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .26, .27}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199953 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 2.0, 2.1}, WorkingPrecision -> 110]

%t RealDigits[r]  (* A199954 *)

%o (PARI) a=1; b=1; c=4; solve(x=2, 2.1, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 22 2018

%Y Cf. A199949.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Nov 12 2011