I'm trying to prove . I'm driving myself crazy trying to figure out what N should be.
so Okay to drop the abs value,
But the left side is undefined at , and worse...it could be negative or positive. So I don't think I can proceed, right? I don't think I need to consider cases, so I think I've already done something wrong. I've tried switching the terms in the distance formula, but I end up with a similar problem (left side could be positive or negative, so I can't square it without losing the inequality).
This is interesting because as , if one solves for one gets for all .
Let's do it :
Expanding we get thus
EDIT : (*) which is always true.
Thanks to both! I gotta get to the point that I can see these simplifications right away. flying squirrel -> unfortunately, we don't have derivatives yet so I don't think I'd get credit for this approach. (Edit...heh... I didn't notice your edit, so I think it's fine...thanks!)