A199284 Decimal expansion of x>0 satisfying 3*x^2+x*cos(x)=3.

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

Offset

0,1

Comments

See A199170 for a guide to related sequences. The Mathematica program includes a graph.

Links

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

Example

negative: -1.081411597194677548285153751592164...
positive:  0.901983106002417964495821536577097...

Mathematica

a = 3; b = 1; c = 3;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -1.1, -1.0}, WorkingPrecision -> 110]
RealDigits[r]    (* A199283 *)
r = x /. FindRoot[f[x] == g[x], {x, .9, 1}, WorkingPrecision -> 110]
RealDigits[r]    (* A199284 *)

Crossrefs

Cf. A199170.

Sequence in context: A256036 A065471 A310000 * A189186 A221429 A221507

Adjacent sequences: A199281 A199282 A199283 * A199285 A199286 A199287

Keyword

nonn,cons

Author

Clark Kimberling, Nov 05 2011

Status

approved