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A199172 Decimal expansion of x<0 satisfying x^2+x*cos(x)=2. 3

%I #5 Mar 30 2012 18:57:57

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

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

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

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

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

%e negative: -1.4669783053971235684198141847804443...

%e positive: 1.2766713679407605540915074904412102...

%t a = 1; b = 1; c = 2;

%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, -1.5, -1.3}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199172 *)

%t r = x /. FindRoot[f[x] == g[x], {x, 1.27, .28}, WorkingPrecision -> 110]

%t RealDigits[r] (* A199173 *)

%Y Cf. A199170.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Nov 04 2011

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)