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

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Homework Help Overview

The discussion revolves around the limit of the expression 2/x as x approaches 0 from the left. Participants are exploring the implications of the limit's behavior and its classification as "does not exist."

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the reasoning behind the limit approaching negative infinity and why it is classified as "does not exist." There is also a query regarding the limit from the right and its relevance to the left-sided limit being discussed.

Discussion Status

Some participants are clarifying the distinction between one-sided limits and the overall limit, noting that the limit from the right is not pertinent to the original question. There is an acknowledgment of the confusion regarding the interpretation of limits approaching infinity.

Contextual Notes

There is a focus on the specific nature of one-sided limits and the implications of stating that a limit approaches infinity. Participants are navigating the definitions and assumptions related to limits in this context.

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: [itex]\lim_{x\to 0^-}[/itex].
 
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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