Recent content by PvtBillPilgrim3

Homework Statement For a given epsilon e > 0, I need to find a delta d such that for all x, abs(x) < d: abs([(x^2 - x + 1)/(x+1)] - 1) < e Homework Equations The Attempt at a Solution I get the absolute value of: x^2 - 2x --------, which is less than or equal to the absolute...

This isn't a copy of my assignment, but I found the exact same question on the web: http://www.math.auckland.ac.nz/~waldron/730/1.pdf It's question 1 on the PDF. I've been trying all night to find inequalties that are strict like it asks for in that particular problem. I don't need help...

OK. I think I figured it out mostly, but I still don't see how the given inequality shows that (an+1 − an) is an increasing sequence. It holds when I take examples, but why for an arbitrary bounded one?

Ok, that makes sense but what makes the limit have to be zero? I guess I don't know how to answer your question. Why can't it be non-zero? If a[SIZE="1"]n is bounded, does that mean a[SIZE="1"]n+1 - a[SIZE="1"]n is bounded also? How do I show it's bounded?

Let (a[SIZE="1"]n) be a bounded sequence. If 2a[SIZE="1"]n <= a[SIZE="1"]n+1 + a[SIZE="1"]n−1, prove that limit n to infinity of (a[SIZE="1"]n+1 − a[SIZE="1"]n) = 0. This question is on my exam review sheet for an elementary analysis class and I'm not really sure where to start. Could...