Why Does the Limit of \(x^2 - \frac{1}{x}\) as \(x\) Approaches 0 Not Exist?

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Homework Help Overview

The discussion revolves around the limit of the expression \(x^2 - \frac{1}{x}\) as \(x\) approaches 0, focusing on the implications of undefined behavior in limits.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the reasoning behind the limit's existence, questioning whether the undefined nature of \(\frac{1}{x}\) at \(x = 0\) affects the limit. Some participants suggest that the behavior of the function near the point is crucial to understanding the limit.

Discussion Status

The discussion includes differing viewpoints on the existence of the limit, with some participants affirming that the limit does not exist while others challenge this conclusion by emphasizing the need to consider the function's behavior around the point of interest.

Contextual Notes

There is an ongoing examination of the definitions and assumptions related to limits, particularly in the context of functions that are undefined at specific points.

carbz
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[SOLVED] Just one more limit problem.

Homework Statement


Find the limit


Homework Equations


\lim_{x \rightarrow 0} (x^2 - \frac{1}{x})


The Attempt at a Solution


I got does not exist for this limit. This is since, when you break it down to two parts, the 1/x is undefined at 0.
 
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That's correct.
 
allright, thank you
 
The fact that a function is undefined at a point does not imply the limit does not exist at that point.
 
It is infinite on both sides of the point, it doesn't exist.
 

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