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Decimal expansion of the greater of two values of x satisfying 4*x^2 - 1 = tan(x) and 0 < x < Pi/2.
3

%I #10 Apr 09 2021 19:05:19

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

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

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

%N Decimal expansion of the greater of two values of x satisfying 4*x^2 - 1 = tan(x) and 0 < x < Pi/2.

%C See A200614 for a guide to related sequences. The Mathematica program includes a graph.

%e lesser: 0.839582259045302941513764008863804986308...

%e greater: 1.350956593976519397744696294368524715373...

%t a = 4; c = 1;

%t f[x_] := a*x^2 - c; g[x_] := Tan[x]

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

%t r = x /. FindRoot[f[x] == g[x], {x, .6, .7}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200616 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]

%t RealDigits[r] (* A200617 *)

%Y Cf. A200614, A200616.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 20 2011