A200279 Decimal expansion of least x satisfying 3*x^2 - 4*cos(x) = 2*sin(x), negated.

7, 3, 5, 6, 3, 8, 0, 7, 6, 4, 4, 4, 6, 8, 2, 0, 8, 6, 1, 4, 7, 7, 6, 9, 5, 5, 6, 1, 2, 3, 1, 1, 6, 8, 1, 9, 6, 8, 7, 7, 6, 5, 5, 3, 8, 3, 9, 9, 4, 8, 2, 5, 4, 5, 9, 7, 7, 0, 5, 1, 1, 3, 8, 7, 9, 4, 5, 8, 4, 1, 7, 8, 0, 7, 1, 9, 1, 9, 7, 3, 5, 5, 2, 8, 4, 2, 2, 0, 3, 5, 6, 5, 9, 2, 8, 5, 8, 5, 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: -0.73563807644468208614776955612311...
greatest x: 1.096406992421267947221987681314...

Mathematica

a = 3; b = -4; c = 2;
f[x_] := a*x^2 + b*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.74, -.73}, WorkingPrecision -> 110]
RealDigits[r]  (* A200279 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.0, 1.1}, WorkingPrecision -> 110]
RealDigits[r]   (* A200280 *)

Prog

(PARI) a=3; b=-4; c=2; solve(x=-1, 0, a*x^2 + b*cos(x) - c*sin(x)) \\ G. C. Greubel, Jul 07 2018

Crossrefs

Cf. A199949.

Sequence in context: A304658 A253298 A155987 * A213085 A119714 A154889

Adjacent sequences: A200276 A200277 A200278 * A200280 A200281 A200282

Keyword

nonn,cons

Author

Clark Kimberling, Nov 15 2011

Status

approved