We know that .
Using continuity make each of the two on the right .
I don't get the reference to . I think you mean choose so that . Otherwise looks fine.
Yes this is the triangle inequlaity and Plato made a slight typo, it should beAlso,
Is that triangle inequality? How did you recognize that you could do this? What happens when you substitute c for y?
Thanks
So heres what I have, I'm not sure about my logic at one step (I point it out where it is)
We know that . I feel like choosing because I feel like it will be east to pick my delta to cancel the 2 (is this logic correct?). Now, choosing a delta to get rid of the 2 in the , I chose delta so that and . Then I can take because this will still be . But then we can say that because really, is just some . (THIS is the part that I'm not sure on. Is y just some c?) Then we get
Ok, trying again, please tell me what you think
We know that . Because is continuous at , I can make arbitrarily small so that and
Now, choosing a delta to get rid of the 2 in the , I chose delta so that and . Then I can take because this will still be . But then we can say that because really, is just some . (THIS is the part that I'm not sure on. Is y just some c?) Then we get [/quote]