The iteration defined by , where ,
has two fixed points where . Show that
and deduce that . How does the iteration behave for other values of ?
attempt at solution:
we have that,
I am a bit confused regarding the limit-question. If and it means that could be any number larger than 1 but smaller than . I figure that I could then choose some such that , in other words we would be moving away from .
Now if instead of , I could see how .
As I rarely have the insight to find errors in problems, I'm sure there's something I'm not getting here, and therefore I ask for you help.