Lim x-->0-: 2/x Does Not Exist

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The limit of 2/x as x approaches 0 from the left does not exist because it approaches negative infinity. The discussion clarifies that stating a limit equals infinity or negative infinity indicates that the limit does not exist in a conventional sense. The focus is specifically on the left-hand limit, which is distinct from the right-hand limit. Misunderstandings about one-sided limits are addressed, emphasizing the importance of context in limit evaluations. Overall, the conclusion is that the limit from the left does not yield a defined value.
Miike012
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Lim 1/x - 1/abs(x)
x -->0-

= 2/x

as x approaches 0- , 2/x approaches neg infinity...

why isn't this correct? the answer is does not exist.
 
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What is the limit from the right?
 
That is right. "Infinity" is not a number. Saying that a limit is "infinity" or "negative infinity" is just saying that the limit does not exist for a particular reason.

verty, the limit from the right is not relevant. The problem specifically asks for the limit from the left: \lim_{x\to 0^-}.
 
I apologise, I thought Mike was asking, why isn't this the limit, but he meant, why isn't this the one-sided limit.
 

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