AP Calculus BC Unit 1: Limits and Continuity

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

Covered syllabus points

1.1 Introducing Calculus: Can Change Occur at an Instant?1.2 Defining Limits and Using Limit Notation 1.3 Estimating Limit Values from Graphs 1.4 Estimating Limit Values from Tables 1.5 Determining Limits Using Algebraic Properties of Limits 1.6 Determining Limits Using Algebraic Manipulation 1.7 Selecting Procedures for Determining Limits 1.8 Determining Limits Using the Squeeze Theorem 1.9 Connecting Multiple Representations of Limits 1.10 Exploring Types of Discontinuities 1.11 Defining Continuity at a Point 1.12 Confirming Continuity over an Interval 1.13 Removing Discontinuities 1.14 Connecting Infinite Limits and Vertical Asymptotes 1.15 Connecting Limits at Infinity and Horizontal Asymptotes 1.16 Working with the Intermediate Value Theorem (IVT)

[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） $\lim _{x \rightarrow 2^{-}} f(x)=3$

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

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

（D） $\lim _{x \rightarrow \infty} f(x)=0$

[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 $\lim _{x \rightarrow 3} \frac{(f(x))^{2}-3 h(x)}{g(x)+h(x)}$ .

$-\frac{1}{5}$

$\frac{1}{2}$

nonexistent

Figure for Question Unit 1: Limits and Continuity question 2 — AP Calculus BC

[Maximum number: 1]

If a is a nonzero constant, then $\lim _{x \rightarrow a} \frac{x-a}{a^{2}-x^{2}}$ is

$-\frac{1}{2 a}$

$-\frac{1}{a}$

nonexistent

Figure for Question Unit 1: Limits and Continuity question 3 — AP Calculus BC

[Maximum number: 1]

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

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

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

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

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

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Covered syllabus points

Unit 1: Limits and Continuity question 1

Unit 1: Limits and Continuity question 2

Unit 1: Limits and Continuity question 3

Unit 1: Limits and Continuity question 4