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Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = sin(x), negated.
3

%I #13 Jul 06 2018 03:03:36

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

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

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

%N Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = sin(x), negated.

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

%H G. C. Greubel, <a href="/A200277/b200277.txt">Table of n, a(n) for n = 0..10000</a>

%e least x: -0.81771521879230454511191454208365777...

%e greatest x: 1.000303639283590185187225035744180...

%t a = 3; b = -4; c = 1;

%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, -.82, -.81}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200277 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200278 *)

%o (PARI) a=3; b=-4; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ _G. C. Greubel_, Jul 05 2018

%Y Cf. A199949.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 15 2011