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A function [math]f[/math] is said to have a removable discontinuity if it is not continuous at [math]a[/math], but can be assigned a value [math]f(a)[/math] [or possibly reassigned a new value [math]f(a)[/math]] such that it becomes continuous there.

• Locate the removable discontinuities in Problem Exercise.
• Show that the only discontinuities a rational function can have are either removable or infinite. That is, if [math]r(x)[/math] is a rational function that is not continuous at [math]a[/math], show that either [math]a[/math] is a removable discontinuity or [math]\lim_{x \goesto a} |r(x)| = + \infty[/math].