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Decimal expansion of least x satisfying 2*x^2 - cos(x) = sin(x), negated.

G. C. Greubel, <a href="/A200107/b200107.txt">Table of n, a(n) for n = 0..10000</a>

(PARI) a=2; b=-1; c=1; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 25 2018

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_Clark Kimberling (ck6(AT)evansville.edu), _, Nov 13 2011

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allocated for Clark KimberlingDecimal expansion of least x satisfying 2*x^2-cos(x)=sin(x).

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

0,1

See A199949 for a guide to related sequences. The Mathematica program includes a graph.

least x: -0.4690323711198093057335493058025105005500...

greatest x: 0.84026351771576789934797349964835579736...

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

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

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

r = x /. FindRoot[f[x] == g[x], {x, -.47, -.46}, WorkingPrecision -> 110]

RealDigits[r] (* A200107 *)

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

RealDigits[r] (* A200108 *)

Cf. A199949.

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nonn,cons

Clark Kimberling (ck6(AT)evansville.edu), Nov 13 2011

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allocated for Clark Kimberling

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