CourseCourseConceptConceptDocsDocuments

AP Calculus BC Unit 1 Limits and Continuity Questions

Practice AP Calculus BC Unit 1 questions on representing limits, analyzing continuity and asymptotes, and applying the Intermediate Value Theorem.

Syllabus
Effective Fall 2025
Course
AP Calculus BC

Covered syllabus points

1.1 Introducing Calculus: Can Change Occur at an Instant?1.2 Defining Limits and Using Limit Notation1.3 Estimating Limit Values from Graphs1.4 Estimating Limit Values from Tables1.5 Determining Limits Using Algebraic Properties of Limits1.6 Determining Limits Using Algebraic Manipulation1.7 Selecting Procedures for Determining Limits1.8 Determining Limits Using the Squeeze Theorem1.9 Connecting Multiple Representations of Limits1.10 Exploring Types of Discontinuities1.11 Defining Continuity at a Point1.12 Confirming Continuity over an Interval1.13 Removing Discontinuities1.14 Connecting Infinite Limits and Vertical Asymptotes1.15 Connecting Limits at Infinity and Horizontal Asymptotes1.16 Working with the Intermediate Value Theorem (IVT)

Question 1

[Maximum number: 1]
Graph of \(f\)

Graph of \(f\)

76．The graph of the function f is shown in the figure above．Which of the following statements must be false？

A

（A） lim⁡x→2−f(x)=3\lim _{x \rightarrow 2^{-}} f(x)=3

B

（B） lim⁡x→2+f(x)=∞\lim _{x \rightarrow 2^{+}} f(x)=\infty

C

（C） lim⁡x→2f(x)=f(2)\lim _{x \rightarrow 2} f(x)=f(2)

D

（D） lim⁡x→∞f(x)=0\lim _{x \rightarrow \infty} f(x)=0

Question 2

[Maximum number: 1]

The functions f(x), g(x), and h(x) have derivatives of all orders. Listed above are values for the functions and their first and second derivatives at x=3. Find lim⁡x→3(f(x))2−3h(x)g(x)+h(x)\lim _{x \rightarrow 3} \frac{(f(x))^{2}-3 h(x)}{g(x)+h(x)}.

A

−15-\frac{1}{5}

B

12\frac{1}{2}

C

1

D

nonexistent

Figure for Question 2 — AP Calculus BC

Question 3

[Maximum number: 1]

If a is a nonzero constant, then lim⁡x→ax−aa2−x2\lim _{x \rightarrow a} \frac{x-a}{a^{2}-x^{2}} is

A

0

B

−12a-\frac{1}{2 a}

C

−1a-\frac{1}{a}

D

nonexistent

Figure for Question 3 — AP Calculus BC

Question 4

[Maximum number: 1]

The graphs of the functions f and g are shown in the figures above. Which of the following statements is false?

A

lim⁡x→1f(x)=0\lim _{x \rightarrow 1} f(x)=0

B

lim⁡x→2g(x)\lim _{x \rightarrow 2} g(x) does not exist.

C

lim⁡x→1(f(x)g(x+1))\lim _{x \rightarrow 1}(f(x) g(x+1)) does not exist.

D

lim⁡x→1(f(x+1)g(x))\lim _{x \rightarrow 1}(f(x+1) g(x)) exists.

All question bank results loaded