This should've been an easy problem for me, though a few small details make it tougher than I'd initially thought.

Let be defined as follows:(this is the main part that has me stumped right now)

for all unless ,

for all where .

Show that as on any straight line through .

Determine if exist as .

If I were to get past that little hurdle in terms of the definition of , I could probably get through the rest using epsilon-delta proofs.