A199606 Decimal expansion of greatest x satisfying x^2+3*x*cos(x)=sin(x).

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..99.

Example

least: -0.93049500263597010976334102402547851258644...
greatest:  3.01796308106862887266781443388576897037832...

Mathematica

a = 1; b = 3; c = 1;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -1.5, 3.5}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
RealDigits[r]  (* A199605, least of 4 roots *)
r = x /. FindRoot[f[x] == g[x], {x, 3, 3.1}, WorkingPrecision -> 110]
RealDigits[r]  (* A199606, greatest of 4 roots *)

Crossrefs

Cf. A199597.

Sequence in context: A137680 A248722 A201663 * A182472 A285867 A349780

Adjacent sequences: A199603 A199604 A199605 * A199607 A199608 A199609

Keyword

nonn,cons

Author

Clark Kimberling, Nov 08 2011

Status

approved