AP Calculus AB · Unit 1: Limits and Continuity
1.8 Determining Limits Using the Squeeze Theorem
In short
You are expected to understand and apply the squeeze theorem to find the limits of functions. The course framework explicitly highlights using the squeeze theorem to demonstrate two foundational trigonometric limits: the limit of (sin x)/x as x approaches 0 is 1, and the limit of (1 - cos x)/x as x approaches 0 is 0.
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What else do you need to know about Determining Limits Using the Squeeze Theorem?
A key emphasis is placed on confirming that the hypotheses or conditions of the squeeze theorem are fully satisfied before it is applied.
Can you do these?
- I can use definitions, theorems, and properties to justify claims about limits.
- I can determine the limits of functions using the squeeze theorem.
- I can find the limit of a function by applying the squeeze theorem and verifying its conditions.
How is Determining Limits Using the Squeeze Theorem tested on the exam?
On the AP Exam, you must establish the practice of explicitly verifying that a theorem's hypotheses are satisfied before applying the theorem. When using the squeeze theorem in free-response questions, you should clearly state and confirm the bounding conditions (the inequalities) and the limits of the outer functions before concluding the limit of the inner function. Failure to explicitly write relevant given information or verify conditions before drawing the conclusion is a common you misunderstanding that examiners penalize.
Free practice questions with full explanations, and instant marking of your free-response answers.
Determining Limits Using the Squeeze Theorem: common questions
What do you need to know about Determining Limits Using the Squeeze Theorem for AP Calculus AB?
You are expected to understand and apply the squeeze theorem to find the limits of functions. The course framework explicitly highlights using the squeeze theorem to demonstrate two foundational trigonometric limits: the limit of (sin x)/x as x approaches 0 is 1, and the limit of (1 - cos x)/x as x approaches 0 is 0.
How is Determining Limits Using the Squeeze Theorem tested on the AP Calculus AB exam?
On the AP Exam, you must establish the practice of explicitly verifying that a theorem's hypotheses are satisfied before applying the theorem. When using the squeeze theorem in free-response questions, you should clearly state and confirm the bounding conditions (the inequalities) and the limits of the outer functions before concluding the limit of the inner function.
How do I know I have mastered Determining Limits Using the Squeeze Theorem?
Check you can do each of these: use definitions, theorems, and properties to justify claims about limits; determine the limits of functions using the squeeze theorem; find the limit of a function by applying the squeeze theorem and verifying its conditions.
Where does Determining Limits Using the Squeeze Theorem fit in AP Calculus AB?
Determining Limits Using the Squeeze Theorem is topic 1.8 in Unit 1: Limits and Continuity of AP Calculus AB.
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