AP Calculus AB Evaluating Limits Algebraically Quiz: 10 Questions with Explanations

AP Calculus AB math quiz: Evaluating Limits Algebraically – Maths PDF

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This limit algebra quiz for AP Calculus AB covers evaluating limits algebraically (Common Core AP CALC AB 1.5, AP CALC AB 1.6, AP CALC AB 1.7, AP CALC AB 1.8), with a free PDF to print.

Test yourself on evaluating limits with substitution, factoring, conjugates, special trig limits and the Squeeze Theorem with 10 multiple-choice questions. Pick one answer for each question, then read the explanation to see why it is right and which common mistake the other choices represent.

AP Calculus AB · Common Core State Standards: AP CALC AB 1.5, AP CALC AB 1.6, AP CALC AB 1.7, AP CALC AB 1.8

Limit algebra quiz: 10 questions

Question 1

The graph of (x² − 4)/(x − 2).

What is \(\lim_{x\to 2} \frac{x^{2}-4}{x-2}\)?

Question 2

What is \(\lim_{x\to 3} (2x^{2}-5x)\)?

Question 3

Values of sin x / x.

According to the table, what does \(\lim_{x\to 0} \frac{\sin x}{x}\) equal?

Question 4

x² sin(1/x) between ±x².

Which theorem proves that \(\lim_{x\to 0} x^{2}\sin\frac{1}{x}=0\)?

Question 5

What is \(\lim_{x\to 0} \frac{\sin 4x}{x}\)?

Question 6

What is \(\lim_{x\to 2}\frac{x^{2}-4}{x^{2}-5x+6}\)?

Question 7

Suppose \(\lim_{x\to 1} f(x)=4\). What is \(\lim_{x\to 1}[f(x)]^{2}-3\)?

Question 8

What is \(\lim_{x\to -3} \frac{x^{2}-9}{x+3}\)?

Question 9

For which value of \(k\) does \(\lim_{x\to 2} \frac{x^{2}+kx-8}{x-2}\) exist?

Question 10

Which form means more work is needed to find a limit?

Remember

Direct substitution works when the function is defined and continuous at the target.
The form 0/0 means “simplify more”, not “the limit is 0” and not “does not exist”.
Multiply by the conjugate to remove a square root from a limit.
lim sin(x)/x = 1 and lim (1 – cos x)/x = 0 as x approaches 0 (radians).

How to use this limit algebra quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

Download the limit algebra quiz as a PDF with the button below and keep it with your notes.

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