AP Calculus AB: Limits Involving Infinity and Special Cases — Drill 1

About This Drill

AP Calculus AB: Limits Involving Infinity and Special Cases — 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 at infinity, infinite limits near vertical asymptotes, and one-sided limits, including cases where the limit does not exist. These topics form the foundation of asymptotic behavior in AP Calculus AB.

Questions in This Drill

1. What is \( \lim_{x \to \infty} \dfrac{4x^2 - 3x + 1}{2x^2 + 5} \)?
2. What is \( \lim_{x \to 3^+} \dfrac{5}{x - 3} \)?
3. What is \( \lim_{x \to \infty} \dfrac{6x^3 + 2x}{x^4 - 1} \)?
4. The function \( f \) is defined as \( f(x) = \dfrac{|x - 2|}{x - 2} \). Which of the following correctly describes \( \lim_{x \to 2} f(x) \)?
5. A rational function \( g(x) = \dfrac{3x^2 + 7}{ax^2 + bx + 1} \) has a horizontal asymptote of \( y = \dfrac{3}{5} \). What must be true?