Is f(x) = (x2 + 2)/x a removable singularity?

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Homework Help Overview

The discussion revolves around identifying singularities in the function f(x) = (x² + 2)/x and determining whether they are removable. The subject area pertains to calculus and the analysis of functions.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the identification of singularities, with an initial focus on the point x = 0. Questions arise regarding the nature of the singularity and whether it is removable, prompting further exploration of definitions and implications.

Discussion Status

The conversation is ongoing, with participants sharing insights about singularities and questioning the definitions involved. Some guidance has been offered regarding the concept of removable singularities, but no consensus has been reached on the specific case of f(x).

Contextual Notes

There is a focus on the distinction between the singularity of the function f(x) and simpler forms like x²/x, which may have different characteristics. The discussion also highlights the importance of understanding what it means for a singularity to be removable.

andrey21
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Find any singularities in the following,say whether they are removable or not

f(x) = (x2 + 2)/x


Attempt at a solution

when f(0) = ((0)2 + 2)/0

=2/0 which isn't defined

So 0 is a singularity
 
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Yes, that is correct! So, do you think it's removable or not?
 
I know that:

x2/x has a removable singularity at x=0

So the singularity will be removable here:
 
x^2 / x has a removable singularity at 0, yes. But you aren't dealing with that, you're dealing with (x^2+2)/x. Now, what does it mean for a singularity to be removable?
 
A removable singularity is a point at which the function is undefined.
 

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