AP Calculus AB Flashcards: Estimating Limit Values from Graphs
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
Does the value of f(c) need to be defined for the limit as x approaches c to exist?
No, the limit can exist even if the function is undefined at x=c. The limit is concerned with the value the function approaches, not its actual value.
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Does the value of f(c) need to be defined for the limit as x approaches c to exist?
No, the limit can exist even if the function is undefined at x=c. The limit is concerned with the value the function approaches, not its actual value.
What does it mean if a limit does not exist at a particular x-value?
It means the function does not approach a single, finite y-value as x approaches that point from both sides.
What is the relationship between a limit and one-sided limits?
The overall limit of a function at a point exists if and only if the left-sided limit and the right-sided limit are equal to each other.
Why can estimating limits from graphs sometimes be misleading?
Because of issues of scale, a graphical representation may not show important function behavior, such as a very small hole or a jump discontinuity.
If a computer-generated graph looks like a perfectly smooth curve, what potential issue must you still consider when estimating a limit?
You must consider that issues of scale might hide important behavior, as the graphing window may not be small enough to show a discontinuity.
What does it mean to estimate the limit of a function from a graph?
It means using the visual information from a function's graph to determine the y-value the function approaches as x gets closer to a particular value.
What is the primary tool used to estimate limits when given a function's plot?
Graphical information is the primary tool used to estimate the value a function approaches at a particular value of x.
How do you use a graph to estimate a one-sided limit from the left?
You trace the function's curve as you approach the target x-value from the left side and observe the y-value the function gets closer to.
What are one-sided limits?
One-sided limits describe the y-value a function approaches as x gets closer to a specific value from either the left side or the right side.
On a graph, the function approaches y=2 from the left of x=4 and y=2 from the right of x=4, but there is a hole at (4,2). What is the limit as x approaches 4?
The limit as x approaches 4 is 2. The limit is the value the function approaches, not the actual value at the point.
Identify a type of function behavior on a graph where the limit would not exist.
A limit does not exist at a jump discontinuity, where the left-sided limit is different from the right-sided limit.