A200288 Decimal expansion of greatest x satisfying 4*x^2 - cos(x) = 2*sin(x).

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

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: -0.300931885421902370031006240717514956...
greatest x: 0.7193842604598758321075524115913806...

Mathematica

a = 4; b = -1; c = 2;
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, -.31, -.30}, WorkingPrecision -> 110]
RealDigits[r]    (* A200287 *)
r = x /. FindRoot[f[x] == g[x], {x, .71, .72}, WorkingPrecision -> 110]
RealDigits[r]   (* A200288 *)

Prog

(PARI) a=4; b=-1; c=2; solve(x=0, 1, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 07 2018

Crossrefs

Cf. A199949.

Sequence in context: A364501 A069609 A019855 * A117493 A177515 A196825

Adjacent sequences: A200285 A200286 A200287 * A200289 A200290 A200291

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved