AP Calculus BC Unit 1 practice questions: Limits and Continuity
8 original multiple-choice questions on AP Calc BC Unit 1, limits and continuity. Answer each one in your browser and read the explanation, then review the key ideas below.
Question 1 of 8
Evaluate lim (x→0) of sin(5x)/x.
Question 2 of 8
f(x) = (x² − 9)/(x − 3) for x ≠ 3. What value of f(3) makes f continuous at x = 3?
Question 3 of 8
Evaluate lim (x→∞) of (3x² + 1)/(5x² − x).
Question 4 of 8
Evaluate lim (x→2) of (x² − 4)/(x − 2).
Question 5 of 8
What is lim (x→0⁺) of 1/x?
Question 6 of 8
f is continuous on [1, 3] with f(1) = −2 and f(3) = 5. Which must be true?
Question 7 of 8
What is the horizontal asymptote of y = (2x + 1)/(x − 3)?
Question 8 of 8
Evaluate lim (x→0) of x²·sin(1/x).
Key ideas in Unit 1
- A limit describes the value f(x) approaches, not necessarily f(a) itself. Check one-sided limits when a function jumps or has an asymptote.
- Algebra first: factor, rationalize or simplify to remove a 0/0 form, and use the squeeze theorem for oscillating functions.
- f is continuous at a when lim f(x) as x→a exists and equals f(a). Removable, jump and infinite discontinuities each break a different part of that.
- Limits at infinity give horizontal asymptotes: compare the leading terms of the numerator and denominator.
- The Intermediate Value Theorem needs continuity on a closed interval and guarantees every value between f(a) and f(b) is reached.
More AP Calc BC practice
Unit 2: Differentiation: Definition and Fundamental Properties →
The full AP Calculus BC practice test, all units
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