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

[andrey21]

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

 

[micromass]

Yes, that is correct! So, do you think it's removable or not?

 

[andrey21]

I know that:

x²/x has a removable singularity at x=0

So the singularity will be removable here:

 

[Char. Limit]

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?

 

[andrey21]

A removable singularity is a point at which the function is undefined.