AP Calculus AB Practice Quiz: Estimating Limit Values from Tables
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 7 questions to check your progress.
Question 1 of 7
All Questions (7)
A) 5
B) 4.999
C) 5.001
D) The limit does not exist.
Correct Answer: A
To estimate the limit as x approaches 2, we observe the behavior of f(x) as x gets closer to 2 from both the left and the right. As x approaches 2 from the left (1.9, 1.99, 1.999), f(x) approaches 5. As x approaches 2 from the right (2.1, 2.01, 2.001), f(x) also approaches 5. Since the left-hand and right-hand limits appear to be the same, the best estimate for the limit is 5.
A) 3
B) -2
C) 4
D) The limit does not exist.
Correct Answer: D
As x approaches 3 from the left (x < 3), the values of h(x) approach -2. As x approaches 3 from the right (x > 3), the values of h(x) approach 4. Since the limit from the left (-2) is not equal to the limit from the right (4), the two-sided limit does not exist.
A) 10
B) 8
C) 7.998
D) The limit cannot be determined.
Correct Answer: B
The limit of a function as x approaches a point is determined by the values of the function near that point, not the value of the function at the point itself. As x approaches 4 from both the left and the right, the values of g(x) get closer to 8. The fact that g(4) = 10 does not affect the limit.
A) 0
B) 1
C) Infinity (∞)
D) The limit does not exist.
Correct Answer: D
As x approaches 1 from the left, the values of p(x) are positive and increase without bound (approaching +∞). As x approaches 1 from the right, the values of p(x) are negative and decrease without bound (approaching -∞). Since the function does not approach a single, finite value, the limit does not exist.
A) 3
B) 9
C) 0
D) The limit does not exist.
Correct Answer: B
The question asks for the left-hand limit, lim (x→0⁻) k(x). This means we only need to consider the values of x that are less than 0 and approaching 0. Looking at the table for x = -0.1, -0.01, and -0.001, the corresponding values of k(x) are 9.1, 9.01, and 9.001. These values are approaching 9.
A) -3
B) 0
C) 0.25
D) The limit does not exist.
Correct Answer: C
The numerical information shows that as x approaches -3 from the left side (e.g., -3.1, -3.01), f(x) gets closer to 0.25. As x approaches -3 from the right side (e.g., -2.99, -2.9), f(x) also gets closer to 0.25. Since the function approaches the same value from both sides, the best estimate for the limit is 0.25.
A) 0
B) 0.00544
C) -0.00005
D) The limit does not exist.
Correct Answer: A
Although the sign of q(x) is alternating as x approaches 0 from both the left and the right, the magnitude of q(x) is getting progressively smaller and closer to zero. For example, at x = -0.01, q(x) is 0.0000506, and at x = -0.001, it is -0.00000083. This pattern indicates that the function values are being 'squeezed' toward a single value. The numerical data strongly suggests that the limit is 0.