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Decimal expansion of greatest x satisfying 3*x^2 - 2*cos(x) = 3*sin(x).
G. C. Greubel, <a href="/A200234/b200234.txt">Table of n, a(n) for n = 1..10000</a>
(PARI) a=3; b=-2; c=3; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 30 2018
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_Clark Kimberling (ck6(AT)evansville.edu), _, Nov 14 2011
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allocated for Clark KimberlingDecimal expansion of greatest x satisfying 3*x^2-2*cos(x)=3*sin(x).
1, 0, 9, 2, 9, 6, 1, 3, 1, 2, 6, 1, 9, 6, 9, 4, 2, 6, 9, 6, 4, 3, 3, 8, 2, 9, 1, 2, 5, 5, 6, 6, 2, 2, 1, 9, 2, 9, 1, 4, 5, 1, 8, 5, 8, 8, 1, 8, 0, 2, 8, 9, 8, 8, 9, 9, 6, 1, 7, 6, 3, 5, 6, 9, 6, 8, 9, 4, 4, 7, 6, 1, 6, 7, 6, 3, 4, 5, 1, 0, 2, 5, 1, 1, 5, 0, 5, 4, 3, 1, 2, 2, 5, 4, 0, 3, 8, 6, 4
1,3
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
least x: -0.432052760425723131996383607455372280...
greatest x: 1.0929613126196942696433829125566221...
a = 3; b = -2; c = 3;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.44, -.43}, WorkingPrecision -> 110]
RealDigits[r] (* A200233 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.08, 1.09}, WorkingPrecision -> 110]
RealDigits[r] (* A200234 *)
Cf. A199949.
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Clark Kimberling (ck6(AT)evansville.edu), Nov 14 2011
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