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A198994 Decimal expansion of x>0 satisfying 4*x^2-3*cos(x)=-2.

%I A198994 #8 Feb 07 2025 19:43:55
%S A198994 4,2,7,2,8,3,4,3,8,7,6,8,8,5,5,3,6,4,0,0,5,4,4,7,7,8,3,5,6,9,8,1,1,7,
%T A198994 2,4,9,1,4,0,6,9,6,7,9,9,8,9,0,2,5,1,1,8,8,9,1,1,1,1,7,2,4,8,9,4,0,8,
%U A198994 5,5,1,4,4,9,9,3,8,0,4,3,7,2,2,6,2,5,2,7,8,4,8,7,7,7,2,7,1,6,3
%N A198994 Decimal expansion of x>0 satisfying 4*x^2-3*cos(x)=-2.
%C A198994 See A198755 for a guide to related sequences. The Mathematica program includes a graph.
%H A198994 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A198994 0.42728343876885536400544778356981172491406...
%t A198994 a = 4; b = -3; c = -2;
%t A198994 f[x_] := a*x^2 + b*Cos[x]; g[x_] := c
%t A198994 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A198994 r = x /. FindRoot[f[x] == g[x], {x, .42, .43}, WorkingPrecision -> 110]
%t A198994 RealDigits[r]  (* A198994 *)
%Y A198994 Cf. A198755.
%K A198994 nonn,cons
%O A198994 0,1
%A A198994 _Clark Kimberling_, Nov 01 2011