AP Calculus AB: Evaluating Limits Algebraically — Drill 1

About This Drill

AP Calculus AB: Evaluating Limits Algebraically — Drill 1 is a Math practice drill covering Limits and Continuity. It contains 5 original questions created by Brian Stewart, a Barron's test prep author with over 20 years of tutoring experience.

Practice evaluating limits algebraically using direct substitution, factoring, and rationalization. These AP Calculus AB skills are essential for Unit 1 and appear throughout both the multiple-choice and free-response sections of the exam.

Questions in This Drill

1. What is \( \lim_{x \to 2} \dfrac{x^3 - 3x + 5}{x^2 + 1} \)?
2. What is \( \lim_{x \to 4} \dfrac{x^2 - 16}{x - 4} \)?
3. What is \( \lim_{x \to 1} \dfrac{x^3 - 1}{x - 1} \)?
4. What is \( \lim_{x \to 9} \dfrac{\sqrt{x} - 3}{x - 9} \)?
5. A student evaluates \( \lim_{x \to 5} \dfrac{x^2 - 25}{x - 5} \) and writes: “Since substituting \( x = 5 \) gives \( \dfrac{0}{0} \), the limit does not exist.” Which of the following best describes the student’s error?