|
|
A200013
|
|
Decimal expansion of greatest x satisfying x^2 - cos(x) = 2*sin(x).
|
|
3
|
|
|
1, 4, 5, 0, 9, 3, 8, 4, 4, 9, 6, 3, 4, 9, 7, 4, 4, 3, 1, 1, 2, 8, 2, 8, 5, 5, 7, 6, 6, 9, 0, 3, 5, 7, 7, 3, 8, 9, 4, 4, 7, 4, 8, 7, 0, 1, 1, 5, 3, 4, 6, 3, 9, 8, 7, 6, 5, 4, 2, 3, 5, 8, 6, 2, 6, 2, 9, 6, 1, 9, 2, 8, 4, 3, 0, 8, 1, 3, 5, 0, 5, 9, 1, 7, 2, 0, 8, 4, 3, 0, 4, 9, 7, 0, 9, 4, 6, 6, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
See A199949 for a guide to related sequences. The Mathematica program includes a graph.
|
|
LINKS
|
|
|
EXAMPLE
|
least x: -0.3941241928589759600997053993545900...
greatest x: 1.450938449634974431128285576690357...
|
|
MATHEMATICA
|
a = 1; b = -1; c = 2;
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, -.4, -.3}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 1.4, 1.5}, WorkingPrecision -> 110]
|
|
PROG
|
(PARI) a=1; b=-1; c=2; solve(x=1, 2, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jun 23 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|