Limit of Function at (-1,3): Does it Exist?

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Homework Help Overview

The discussion revolves around the limit of a function as x approaches -1, particularly at the point (-1, 3). Participants are examining whether the limit exists when the function's value at that point is not defined.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the existence of the limit as x approaches -1, discussing the implications of the function's value at that point. There are inquiries about the behavior of the function from both sides of -1 and the relevance of the function's value at that specific point.

Discussion Status

The discussion is ongoing, with various interpretations being explored. Some participants are providing insights into the nature of limits, while others are questioning specific assumptions regarding the function's values. There is no explicit consensus yet, but productive dialogue is occurring.

Contextual Notes

Participants are navigating the implications of the function's value at (-1, 3) being undefined and how that affects the limit's existence. There are references to specific points in the function that may influence the discussion.

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Homework Statement


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Homework Equations


The Attempt at a Solution


If the dot (-1,3) is gone, does the limit of x->-1 exist??
 
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How do you conclude lim x->(-1)+ is 3? And why do you think lim x->(-1) doesn't exist?
 


Yeah, you should check E and F
you got f wrong because e is wrong
for e, why did you say that the answer is 3
if the question was f(-1) = ?, then the answer would be 3
 


no.., just ignore the answer
I know x->(-1)+ is 1
but is x->(-1) exist ,if the dot is gone?
 


Yes. The limit as x goes to a from below or above, or the limit as x goes to a, all depend only on the values of f(x) for x close to a, not at a. The value of f(a) is irrelevant to [/math]\lim_{x\to a} f(x)[/math] which may exist even if f(a) does not exist.
 

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