I am to use the delta-epsilon definition of a limit to show that the following limit does not exist. Unfortuantely, neither my instructor nor my textbook offer any worked examples or guides as to do this so I have been quite disillusioned so far. I have posted my attempt at a proof below.
Thank you very much for your help.
Prove that does not exist.
Proof #1: I came up with this but I don't think that it works because x depends solely on L. I think that delta should be in my somewhere since I have to show that for any , the definition of a limit does not hold.
If I am indeed right about this problem, how should I modify my proof?
My course assumes that a limit which goes to is the same as a limit that does not exist. Although I can show that DNE by evaluating the right- and left-hand limits, I have to show that it does not exist using the delta-epsilon definition of a limit and my attempt is in my first post.
Therefore, could my proof above be reviewed? I really am uncertain as to whether it is valid.