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Given any function where you're asked to find all points of discontinuity and to classify those points, is there a quick way to look at it and tell if that discontinuity is removable or not?

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up vote 10 down vote accepted

A removable discontinuity occurs precisely when the left hand and right hand limits exist as equal real numbers but the value of the function at that point is not equal to this limit because it is another real number.

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So, in all other cases, it is non-removable? Like if one or more of the limits (left vs right) are $\infty$? – agent154 Dec 11 '12 at 2:30
Even of both side limits are $\infty$ the discontinuity is not removable because you cannot set the value of the function at that point to be $\infty$. – lhf Dec 11 '12 at 2:35
Thank you both for the help. This should help my review for tomorrow's final exam. – agent154 Dec 11 '12 at 2:38

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