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A200296 Decimal expansion of greatest x satisfying 4*x^2 - 2*cos(x) = 3*sin(x). 3
9, 4, 9, 1, 4, 5, 7, 1, 9, 4, 2, 3, 0, 0, 9, 8, 4, 4, 8, 1, 8, 9, 1, 9, 6, 7, 0, 8, 5, 7, 2, 5, 6, 6, 1, 0, 8, 7, 9, 0, 6, 6, 3, 3, 3, 0, 0, 2, 9, 8, 9, 2, 3, 1, 7, 5, 6, 2, 8, 7, 1, 6, 4, 0, 4, 2, 2, 9, 8, 6, 6, 4, 6, 6, 4, 9, 9, 0, 2, 8, 0, 0, 7, 2, 8, 4, 5, 1, 8, 0, 1, 9, 4, 7, 2, 4, 3, 7, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

EXAMPLE

least x: -0.40500714967330681353010125636730...

greatest x: 0.949145719423009844818919670857...

MATHEMATICA

a = 4; b = -2; c = 3;

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

Plot[{f[x], g[x]}, {x, -1, 1}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, -.41, -.40}, WorkingPrecision -> 110]

RealDigits[r]   (* A200295 *)

r = x /. FindRoot[f[x] == g[x], {x, .94, .95}, WorkingPrecision -> 110]

RealDigits[r]   (* A200296 *)

PROG

(PARI) a=4; b=-2; c=3; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 08 2018

CROSSREFS

Cf. A199949.

Sequence in context: A103742 A092736 A019617 * A021517 A154977 A203082

Adjacent sequences:  A200293 A200294 A200295 * A200297 A200298 A200299

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 15 2011

STATUS

approved

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Last modified June 15 16:13 EDT 2019. Contains 324142 sequences. (Running on oeis4.)