AP Calculus AB Flashcards: Selecting Procedures for Determining Limits
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 Squeeze Theorem used for in determining limits?
The Squeeze Theorem is used to find the limit of a function by 'squeezing' it between two other functions that share the same, known limit at that point.
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What is the Squeeze Theorem used for in determining limits?
The Squeeze Theorem is used to find the limit of a function by 'squeezing' it between two other functions that share the same, known limit at that point.
Why is it important to practice selecting from multiple procedures to determine limits?
Different functions and indeterminate forms require different algebraic or analytical techniques to be resolved, so one must know when and how to apply the correct procedure.
When evaluating the limit of a piecewise function at the point where the function's rule changes, what procedure must you follow?
You must evaluate the one-sided limits from the left and the right. The overall limit exists only if these two one-sided limits are equal.
What technique is often used for finding the limit of a function involving a square root that results in an indeterminate form?
Multiplying the numerator and denominator by the conjugate of the expression containing the square root is the most common procedure.
What procedure should you consider for a limit of the form lim h→0 of [f(x+h) - f(x)] / h?
This form represents the formal definition of the derivative of f(x). The procedure is to identify the function f(x) and find its derivative, f'(x).
Which procedure is most appropriate for evaluating the limit of a rational function that results in the indeterminate form 0/0?
The primary method is to factor the numerator and denominator to cancel common factors. L'Hôpital's Rule is another valid procedure if derivatives are applicable.
How do you typically determine the limit of a rational function as x approaches positive or negative infinity?
Compare the degrees of the polynomials in the numerator and denominator, or divide every term by the highest power of x in the denominator to analyze the end behavior.
Under what conditions can L'Hôpital's Rule be applied to find a limit?
L'Hôpital's Rule can be applied only when direct substitution results in an indeterminate form of the type 0/0 or ±∞/±∞.
What is the first method you should always attempt when evaluating a limit?
Always try direct substitution first. If this method results in a real number, that is the limit.
What is an "indeterminate form" in the context of limits?
An indeterminate form, such as 0/0 or ∞/∞, is a result from direct substitution that does not provide enough information to determine the limit's value, requiring another procedure.