Bounds for non-linear recursive sequence

[burritoloco]

Homework Statement

We are given the real sequence x_n+1 = (x_n)^2 - 100 + sin(n), some x_0

Prove that if the sequence is bounded with positive numbers, then necessarily
10 <= x_n <= 11 for all n>=0.

Homework Equations

The Attempt at a Solution

I tried induction and it didn't work. Not sure what's the way to go. Thanks for the help!

 

[micromass]

You could prove the following: if there exist an n such that xn<10 of xn>11, then the sequence becomes unbounded or negative. Try a few examples first!

 

[burritoloco]

Worked perfectly. Thanks a lot!