Hello, 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 Let 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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