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A200627 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 4 = tan(x) and 0 < x < Pi/2.

%I A200627 #10 Jan 30 2025 13:17:12
%S A200627 1,4,0,0,1,0,2,5,5,5,3,3,6,9,4,1,7,4,1,8,3,1,9,5,9,3,7,1,5,7,1,5,8,5,
%T A200627 4,7,3,0,5,3,8,8,4,6,9,6,6,3,4,1,9,0,6,0,7,3,0,4,4,3,6,4,3,4,4,5,2,6,
%U A200627 9,3,7,2,9,0,5,1,9,5,1,5,7,0,3,3,9,8,8,1,7,5,6,5,2,3,4,9,1,0,1
%N A200627 Decimal expansion of the greater of two values of x satisfying 5*x^2 - 4 = tan(x) and 0 < x < Pi/2.
%C A200627 See A200614 for a guide to related sequences. The Mathematica program includes a graph.
%H A200627 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A200627 lesser:  1.0862483073723514930516537470257901302111...
%e A200627 greater: 1.4001025553369417418319593715715854730538...
%t A200627 a = 5; c = 4;
%t A200627 f[x_] := a*x^2 - c; g[x_] := Tan[x]
%t A200627 Plot[{f[x], g[x]}, {x, -.1, Pi/2}, {AxesOrigin -> {0, 0}}]
%t A200627 r = x /. FindRoot[f[x] == g[x], {x, .9, 1.0}, WorkingPrecision -> 110]
%t A200627 RealDigits[r]   (* A200626 *)
%t A200627 r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
%t A200627 RealDigits[r]   (* A200627 *)
%Y A200627 Cf. A200614.
%K A200627 nonn,cons
%O A200627 1,2
%A A200627 _Clark Kimberling_, Nov 20 2011