I need help to write a formal proof to show that the following limits do not exist.
1. . i.e. show that is false for .
2. does not exist. i.e. show that is false for .
Thanks in advance
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Consider the right-hand limit .
The points each can be used in that limit. But .
Thus that limit will get greater and greater. So the limit cannot exist.
, such that whenever it necessarily follows that
So, we must find an such that the above will not be satisfied for any . Let .
Looking at L > 0 . Not possible.
Or looking at L < 0
Let's do #2:
Let's assume there is a number L such that .
Then there exists a number such that whenever
In particular, and are two values of x.
Therefore, and or and ,
which is impossible. Therefore, the limit does not exist.
Thank you very much for helping me out
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