Discontinuities refer to points at which a function is not continuous.
Jump Discontinuity
A jump discontinuity occurs when a function has a sudden “jump” at a certain point. The left-hand limit and the right-hand limit at that point exist but are not equal.
Infinite Discontinuity
An infinite discontinuity occurs when the function approaches infinity at a certain point. The limits do not exist as the function tends to positive or negative infinity.
Point Discontinuity (Removable Discontinuity)
A point discontinuity occurs when a function is not defined at a certain point, but the limits from both sides exist and are equal. This type of discontinuity can be “removed” by defining the function at that point.
Oscillatory Discontinuity
An oscillatory discontinuity occurs when the function oscillates between two values as it approaches a point, and thus the limit does not exist.
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