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Decimal expansion of least x satisfying 2*x^2 + cos(x) = 3*sin(x).
3

%I #16 Jun 24 2018 08:57:37

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

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

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

%N Decimal expansion of least x satisfying 2*x^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="/A199967/b199967.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: 0.45041223638324913376478190783839778...

%e greatest x: 0.989450014493949167489788332695714...

%t a = 2; b = 1; c = 3;

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

%t Plot[{f[x], g[x]}, {x, -.1, 2}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, .4, .5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199967 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .98, .99}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200003 *)

%o (PARI) a=2; b=1; c=3; solve(x=0, .5, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jun 23 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 12 2011

%E A-number corrected by _Jaroslav Krizek_, Nov 27 2011