AP Calculus AB Unit 1 Limits and Continuity Questions

Explore AP Calculus Unit 1 questions on limit notation, graphical and numerical limits, continuity, asymptotes, and 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]

$\lim _{x \rightarrow 2^{-}} \frac{|x-2|}{x-2}$ is

$-\infty$

-1

$\infty$

nonexistent

[Maximum number: 1]

$\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=$

$-\frac{4}{\pi^{2}}$

$\frac{2}{\pi}$

[Maximum number: 1]

mit h approaches to 0 of start fraction numerator square root of 25 plus h end root minus 5 over denominator h end fraction

$(\mathrm{A})=0$

(B) als 1 over 10

(D) does not exist

[Maximum number: 1]

Let f and g be the functions defined by $f(x)=\frac{x^{2}-25}{x^{2}-29}$ and $g(x)=\frac{x+5}{2 x+4}$ . If the function h satisfies $f(x) \leq h(x) \leq g(x)$ for $1 \leq x \leq 5$ , what is $\lim _{x \rightarrow 3} h(x)$ ?

$\frac{1}{2}$

$\frac{4}{5}$

The limit cannot be determined from the given information.

All question bank results loaded

Covered syllabus points

Question 1

Question 2

Question 3

Question 4