Hole discontinuity
This original textbook reading covers part of the AP topic. Follow the AP course outline for complete topic instruction and practice.
Glossary and deeper reading · 1 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Removable discontinuity
A removable discontinuity occurs when a finite two-sided limit exists but the function is missing or has a different value at the target. Changing or defining that single value to equal the limit repairs continuity. For example, (x²−1)/(x−1) has a removable discontinuity at 1 and can be repaired by setting its value there to 2. A jump with unequal one-sided limits cannot be repaired this way.