Question

How do you know if a discontinuity is removable or non removable with limits?

Answer 1

it is removable if ... you can remove it
for example you can remove it in \(\frac{x^2-4}{x-2}\) by making it \(x+2\)
you could not remove it in for example \(\frac{1}{x-2}\)

Answer 2

But I have to show it for piecewise functions with limits, so its not that easy.