AP Calculus AB Flashcards: Defining Limits and Using Limit Notation
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 the formal definition of a limit?
The limit of f(x) as x approaches c is a real number R if f(x) can be made arbitrarily close to R by taking x sufficiently close to c (but not equal to c).
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What is the formal definition of a limit?
The limit of f(x) as x approaches c is a real number R if f(x) can be made arbitrarily close to R by taking x sufficiently close to c (but not equal to c).
What are the different ways a limit can be expressed?
A limit can be expressed in multiple ways, including graphically, numerically, and analytically.
What is the standard notation used to represent a limit analytically?
If the limit of a function f(x) as x approaches c exists and is a real number R, the common notation is $\lim_{x\to c}f(x)=R$.
A function g(x) is defined such that $\lim_{x\to -2}g(x)=0$. Describe the behavior of g(x).
As the value of x gets sufficiently close to -2 (but not equal to -2), the value of the function g(x) can be made arbitrarily close to 0.
What does it mean to interpret a limit expressed in analytic notation?
It means to understand and describe the behavior of the function near a specific point based on the formal limit notation, $\lim_{x\to c}f(x)=R$.
What does it mean for a function's value, f(x), to be 'arbitrarily close' to the limit R?
It means we can make the distance between f(x) and R as small as we want, simply by choosing an x-value that is sufficiently close to c.
What is an analytical representation of a limit?
An analytical representation of a limit is the use of correct mathematical notation, like $\lim_{x\to c}f(x)=R$, to formally state the limit of a function.
In the definition of a limit, why is it specified that x is not equal to c?
This condition is specified because the limit describes the behavior of the function as it approaches c, not the actual value of the function at c itself.
Interpret the meaning of the expression $\lim_{x\to c}f(x)=R$.
This expression means that the value of the function, f(x), gets closer and closer to the real number R as the input, x, gets closer and closer to c.
How would you represent the following statement using correct limit notation: 'The limit of a function f(x) as x approaches 7 is 15'?
This statement is represented analytically as $\lim_{x\to 7}f(x)=15$.