

A199614


Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=sin(x).


3



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

1,1


COMMENTS

See A199597 for a guide to related sequences. The Mathematica program includes a graph.


LINKS



EXAMPLE

least: 1.077309917524072030339979615126813664791...
greatest: 3.553241680682892523957265556234494902...


MATHEMATICA

a = 1; b = 4; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, 2, 4}, {AxesOrigin > {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.1, 1.0}, WorkingPrecision > 110]
RealDigits[r] (* A199613, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.5, 3.6}, WorkingPrecision > 110]
RealDigits[r] (* A199614, greatest of 4 roots *)


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



