A199618 Decimal expansion of greatest x satisfying x^2+4*x*cos(x)=3*sin(x).

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

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..98.

Example

least: -0.5535433817860336287020344905911816930...
greatest:  3.4822676247861932090867036675576803...

Mathematica

a = 1; b = 4; c = 3;
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, -.56, -.55}, WorkingPrecision -> 110]
RealDigits[r]  (* A199617, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]  (* A199618, greatest of 4 roots *)

Crossrefs

Cf. A199597.

Sequence in context: A100231 A016609 A346411 * A088745 A213922 A306568

Adjacent sequences: A199615 A199616 A199617 * A199619 A199620 A199621

Keyword

nonn,cons

Author

Clark Kimberling, Nov 08 2011

Status

approved