โˆซcalculus i review

key term - Jump discontinuity

Definition

A jump discontinuity occurs at a point where the left-hand and right-hand limits of a function exist but are not equal. This results in a 'jump' in the graph of the function at that point.

5 Must Know Facts For Your Next Test

  1. At a jump discontinuity, $\lim_{{x \to c^-}} f(x) \neq \lim_{{x \to c^+}} f(x)$.
  2. The function is not continuous at a jump discontinuity.
  3. Both one-sided limits must exist for there to be a jump discontinuity.
  4. A jump discontinuity often appears as a vertical gap in the graph of the function.
  5. Piecewise functions frequently exhibit jump discontinuities.

Review Questions

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