Types of discontinuities | Limits and continuity | AP Calculus AB | Khan Academy

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A function being continuous at a point means that the two-sided limit at that point exists and is equal to the function's value. Point/removable discontinuity is when the two-sided limit exists but isn't equal to the function's value. Jump discontinuity is when the two-sided limit doesn't exist because the one-sided limits aren't equal. Asymptotic/infinite discontinuity is when the two-sided limit doesn't exist because t's unbounded.
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Jump discontinuity is a type of an essential discontinuity. There are two types of essential discontinuity: infinite and jump.

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