Unit 1: Limits and Continuity

AP Calculus AB — 72 practice questions with detailed explanations. Use the links below to open each full question page (ideal for search indexing and deep study).

Unit summary

This unit covers core ideas tested on the AP exam. Each listed item links to a standalone page with the full stem, answer choices where applicable, a step-by-step explanation, and the correct answer. Difficulty labels help you prioritize review.

Questions in this unit

Sample prompts

Short previews of topics covered (not full question text).

  • The position of a particle moving along a straight line is given by s(t) = t³ - …
  • Let f(x) = {x² - 4x + 3 for x < 2; ax + b for x ≥ 2}. For what values of a and b…
  • If lim(h→0) [tan(π/4 + h) - 1]/h represents f'(a) for some function f at some po…
  • A spherical balloon is being inflated. If the radius r is increasing at a consta…
  • For the function h(x) = ln(x)/x², which of the following gives h'(x)?…
  • The limit definition of the derivative of f at x = a is given by lim(h→0) [f(a+h…
  • If g(x) = sin(x)·eˣ, what is g'(0)?…
  • The function f is defined by f(x) = |x - 3| + 2. Which of the following statemen…
  • Let g(x) = |x² − 4|. Which of the following statements about g is true?…
  • If f(x) = √x, what is the value of lim(h→0) [f(4 + h) − f(4)] / h ?…
  • A function f(x) is said to be continuous on the closed interval [a, b] if it is …
  • Consider the function f(x) = 1 / (x - 3). Which of the following statements is t…