AP Calculus BC 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) 2
B) 5.9
C) 6
D) Does not exist
Correct Answer: C
To estimate the limit as x approaches 2, we examine the values of f(x) for x-values very close 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 6. As x approaches 2 from the right (2.1, 2.01, 2.001), f(x) also approaches 6. Since the left-hand and right-hand limits appear to be equal, the best estimate for the limit is 6.
A) -3
B) -5
C) Undefined
D) Does not exist
Correct Answer: B
The limit of a function as x approaches a value does not depend on the function's value at that point. As x approaches -3 from the left, g(x) approaches -5. As x approaches -3 from the right, g(x) also approaches -5. Because the function approaches the same value from both sides, the limit is estimated to be -5.
A) 4
B) 5.5
C) 7
D) Does not exist
Correct Answer: D
To find the limit as x approaches 1, we must check the behavior from both the left and the right. As x approaches 1 from the left (x < 1), the values of h(x) approach 4. This is the left-hand limit. As x approaches 1 from the right (x > 1), the values of h(x) approach 7. This is the right-hand limit. Since the left-hand limit (4) is not equal to the right-hand limit (7), the overall limit does not exist.
A) 0
B) ∞
C) -∞
D) Does not exist
Correct Answer: C
The question asks for the right-hand limit as x approaches 0 (indicated by x→0⁺). We look at the values of k(x) for x > 0 and getting closer to 0. As x takes values 0.1 and 0.01, k(x) takes values -100 and -10000. The values of k(x) are decreasing without bound. Therefore, the limit is estimated to be -∞.
A) 0
B) 1
C) 0.99
D) Does not exist
Correct Answer: B
We examine the behavior of p(x) as x gets closer to 0 from both sides. As x approaches 0 from the left (-0.1, -0.01, -0.001), the values of p(x) get progressively closer to 1. As x approaches 0 from the right (0.1, 0.01, 0.001), the values of p(x) also get progressively closer to 1. Since the function approaches the same value from both directions, the best estimate for the limit is 1.
A) 3
B) 10
C) -2
D) Does not exist
Correct Answer: B
The notation x→5⁻ indicates the limit as x approaches 5 from the left side (values less than 5). Looking at the table for x-values 4.9, 4.99, and 4.999, the corresponding f(x) values are 10.1, 10.01, and 10.001. These values are getting closer and closer to 10. The value of f(5)=3 is irrelevant for finding the limit.
A) lim (x→3) f(x) = -1
B) lim (x→3⁺) f(x) = -1
C) lim (x→3⁻) f(x) = 4
D) lim (x→3) f(x) does not exist
Correct Answer: D
We must evaluate the one-sided limits. For the left-hand limit, as x approaches 3 from the left (2.9, 2.99, 2.999), f(x) approaches -1. So, lim (x→3⁻) f(x) = -1. For the right-hand limit, as x approaches 3 from the right (3.01, 3.001), f(x) approaches 4. So, lim (x→3⁺) f(x) = 4. Since the left-hand limit (-1) and the right-hand limit (4) are not equal, the two-sided limit does not exist.