AP Calculus AB Flashcards: Exploring Types of Discontinuities
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 10 cards to help you master important concepts.
What is a removable discontinuity?
A removable discontinuity is a type of discontinuity where the function has a 'hole' at a point, but the limit as x approaches that point exists.
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What is a removable discontinuity?
A removable discontinuity is a type of discontinuity where the function has a 'hole' at a point, but the limit as x approaches that point exists.
What are the three types of discontinuities mentioned in the content?
The three types of discontinuities are removable discontinuities, jump discontinuities, and discontinuities due to vertical asymptotes.
What is the fundamental basis for any argument about continuity at a point?
The fundamental basis for justifying continuity at a point is the formal definition of continuity.
How do limits help differentiate between a jump discontinuity and a removable discontinuity?
At a removable discontinuity, the two-sided limit exists. At a jump discontinuity, the two-sided limit does not exist because the left and right-sided limits are not equal.
If a function's limit exists at x=c but the function is not continuous there, what type of discontinuity is it?
This describes a removable discontinuity, as the existence of the limit is the key characteristic.
If the limit of g(x) as x approaches 0 is infinite, what type of discontinuity is present at x=0?
The function g(x) has a discontinuity due to a vertical asymptote at x=0.
How must you justify conclusions about a function's continuity at a specific point?
You must justify conclusions about continuity at a point by using the formal definition of continuity.
What is a discontinuity due to a vertical asymptote?
This type of discontinuity occurs where the function approaches infinity or negative infinity as x approaches a certain value, corresponding to a vertical asymptote.
What is a jump discontinuity?
A jump discontinuity occurs when the function 'jumps' from one value to another, meaning the left-hand and right-hand limits at that point exist but are not equal.
The limit of f(x) as x approaches 2 from the left is 5, and the limit as x approaches 2 from the right is 1. What type of discontinuity is at x=2?
The function has a jump discontinuity at x=2 because the one-sided limits exist but are not equal.