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A200007 Decimal expansion of greatest x satisfying 3*x^2 + cos(x) = 4*sin(x). 3
9, 3, 5, 7, 8, 1, 9, 5, 4, 5, 6, 0, 2, 0, 1, 6, 9, 0, 6, 4, 7, 6, 9, 0, 3, 5, 6, 7, 4, 8, 3, 5, 0, 6, 5, 5, 1, 8, 6, 4, 5, 4, 2, 4, 0, 5, 5, 1, 0, 1, 8, 8, 3, 7, 9, 3, 0, 4, 1, 7, 2, 9, 1, 9, 1, 7, 6, 6, 5, 6, 9, 6, 0, 6, 1, 3, 3, 0, 9, 3, 0, 3, 4, 5, 2, 2, 9, 7, 6, 4, 4, 8, 2, 1, 4, 6, 2, 6, 7 (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:  0.31916558449395611450944828046123878...

greatest x: 0.935781954560201690647690356748350...

MATHEMATICA

a = 3; b = 1; c = 4;

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

Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]

r = x /. FindRoot[f[x] == g[x], {x, .31, .32}, WorkingPrecision -> 110]

RealDigits[r]  (* A200006 *)

r = x /. FindRoot[f[x] == g[x], {x, .93, .94}, WorkingPrecision -> 110]

RealDigits[r]  (* A200007 *)

PROG

(PARI) a=3; b=1; c=4; solve(x=.5, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018

CROSSREFS

Cf. A199949.

Sequence in context: A011212 A145924 A324995 * A153618 A171051 A230158

Adjacent sequences:  A200004 A200005 A200006 * A200008 A200009 A200010

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 12 2011

EXTENSIONS

a(89)-a(98) corrected by G. C. Greubel, Jun 23 2018

STATUS

approved

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Last modified September 15 04:09 EDT 2019. Contains 327062 sequences. (Running on oeis4.)