_Clark Kimberling (ck6(AT)evansville.edu), _, Nov 04 2011

OEIS Server: https://oeis.org/edit/global/285

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allocatedDecimal expansion of forx<0 Clarksatisfying Kimberling2*x^2+x*cos(x)=2.

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

1,4

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

negative: -1.11586547417780092002590535253585579273...

positive: 0.84824964906603356449300167136536010515870...

a = 2; b = 1; c = 2;

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

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

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

RealDigits[r] (* A199265 *)

r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]

RealDigits[r] (* A199266 *)

Cf. A199170.

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nonn,cons

Clark Kimberling (ck6(AT)evansville.edu), Nov 04 2011

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