A199276 - OEIS

%I #8 Feb 07 2025 16:44:05

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

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

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

%N Decimal expansion of x>0 satisfying 2*x^2+3*x*cos(x)=2.

%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e negative: -1.25750748269679781262452282006866921022...

%e positive:  0.547005740546889576436923247150755725087...

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

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

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A199275 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .54, .55}, WorkingPrecision -> 110]

%t RealDigits[r]    (* A199276 *)

%Y Cf. A199170.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Nov 04 2011