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A199171 Decimal expansion of x>0 satisfying x^2+x*cos(x)=1. 2

%I

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

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

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

%N Decimal expansion of x>0 satisfying x^2+x*cos(x)=1.

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

%e negative: -1.19835984451866026826502160343030898927268...

%e positive: 0.685174133854503187895211530638458709591...

%t a = 1; b = 1; c = 1;

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

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

%t r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199170 *)

%t r = x /. FindRoot[f[x] == g[x], {x, .68, .69}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199171 *)

%Y Cf. A199170.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Nov 03 2011

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Last modified February 26 04:47 EST 2020. Contains 332276 sequences. (Running on oeis4.)