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

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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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