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A200224 Decimal expansion of greatest x satisfying 3*x^2 - cos(x) = 2*sin(x). 3
8, 4, 8, 9, 0, 5, 1, 8, 8, 3, 2, 9, 5, 2, 2, 3, 6, 1, 7, 3, 4, 5, 6, 3, 8, 1, 6, 2, 6, 6, 1, 3, 2, 6, 7, 6, 8, 3, 4, 5, 9, 5, 3, 3, 8, 7, 9, 9, 7, 8, 6, 6, 5, 2, 5, 8, 0, 4, 1, 9, 1, 3, 6, 6, 3, 5, 7, 5, 7, 3, 3, 0, 4, 0, 5, 9, 1, 3, 7, 2, 4, 9, 5, 3, 8, 3, 2, 3, 5, 4, 5, 6, 3, 8, 6, 2, 5, 8, 6 (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: -0.3231143338862262845356370492311714...

greatest x: 0.84890518832952236173456381626613...

MATHEMATICA

a = 3; b = -1; c = 2;

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, -.33, -.32}, WorkingPrecision -> 110]

RealDigits[r]   (* A200223 *)

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

RealDigits[r]   (* A200224 *)

PROG

(PARI) a=3; b=-1; c=2; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 30 2018

CROSSREFS

Cf. A199949.

Sequence in context: A202998 A110835 A087015 * A124012 A000803 A198063

Adjacent sequences:  A200221 A200222 A200223 * A200225 A200226 A200227

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Nov 14 2011

STATUS

approved

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)