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Epilon-Delta proofs :D

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So I was reviewing a bit for a class on complex variables I have to take next quarter - and one of the requirements is the class on limits infinite series. I took that class quite a while ago and there was no book (notes-only type thing) so as I was going through sample exercises, this got me a bit stumped. As I''m a regular visitor to this forum, I thought to ask. Since it isn''t *technically* homework for a class, I suppose that it''s not against forum rules. Basically the problem is pretty simple - to provide a epsilon-delta proof of: Lim (1/x) = 1/x0 for all x0 != 0 x->x0 When I go to do my epsilon-delta proof, I arrive at: |x - x0|/|x x0| ... which is all well and good, I have my |x-x0| on the top there, so I am almost ready to get my relation between epsilon and delta. However, I can''t figure out how to get rid of the |x| in the denominator. If x0 >= 1, this is easy, but... what if x0 < 1? Is there any way to do this cleanly without breaking the whole thing into two parts (being x0 >=1 and x0 < 1)? Thanks alot.

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Thanks for being considerate of the forum policy. Homework discussions can be okay, as long as you explain yourself (as you did) and show your own work (which you started to do).

Graham Rhodes
Senior Scientist
Applied Research Associates, Inc.

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