ConceptConceptDocsDocuments

AP Calculus AB Unit 1: Limits and Continuity

Explore AP Calculus Unit 1 questions on limit notation, graphical and numerical limits, continuity, asymptotes, and the Intermediate Value Theorem.

Syllabus
Effective Fall 2025
Course
AP Calculus AB

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)

Unit 1: Limits and Continuity question 1

[Maximum number: 1]

lim⁡x→2−∣x−2∣x−2\lim _{x \rightarrow 2^{-}} \frac{|x-2|}{x-2} is

A

−∞-\infty

B

-1

C

∞\infty

D

nonexistent

Unit 1: Limits and Continuity question 2

[Maximum number: 1]

lim⁡x→π2sin⁡xx=\lim _{x \rightarrow \frac{\pi}{2}} \frac{\sin x}{x}=

A

−4π2-\frac{4}{\pi^{2}}

B

0

C

2π\frac{2}{\pi}

D

1

Unit 1: Limits and Continuity question 3

[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

A

(A)=0(\mathrm{A})=0

B

(B) als 1 over 10

C

(C) =1

D

(D) does not exist

Unit 1: Limits and Continuity question 4

[Maximum number: 1]

Let f and g be the functions defined by f(x)=x2−25x2−29f(x)=\frac{x^{2}-25}{x^{2}-29} and g(x)=x+52x+4g(x)=\frac{x+5}{2 x+4}. If the function h satisfies f(x)≤h(x)≤g(x)f(x) \leq h(x) \leq g(x) for 1≤x≤51 \leq x \leq 5, what is lim⁡x→3h(x)\lim _{x \rightarrow 3} h(x) ?

A

12\frac{1}{2}

B

45\frac{4}{5}

C

1

D

The limit cannot be determined from the given information.

Figure for Question Unit 1: Limits and Continuity question 4 — AP Calculus AB
All question bank results loaded