This study guide covers the connection between infinite limits and vertical asymptotes. It reviews prerequisite knowledge of limits and introduces discontinuities, focusing on vertical asymptotes. The guide explains how to identify vertical asymptotes using infinite limits, provides examples and solutions, and offers practice questions with an answer key. Key topics include evaluating limits approaching infinity, identifying asymptotes from equations or graphs, and connecting function behavior near asymptotes to infinite limits.

#AP Calculus AB/BC: Connecting Infinite Limits and Vertical Asymptotes 🚀

Hey there! Let's dive into a crucial topic that bridges limits and discontinuities: vertical asymptotes. This is a key area, so buckle up and let's make sure you've got it down pat!

#🔗 Review: Essential Pre-requisites

Before we get started, make sure you're comfortable with these topics:

1.2: Defining Limits and Using Limit Notation
1.5: Determining Limits Using Algebraic Properties of Limits
1.6: Determining Limits Using Algebraic Manipulation

#⚠️ Understanding Discontinuities

Discontinuities are points where a function is either undefined or behaves erratically. Recognizing these is super important because many calculus theorems only apply to continuous functions. Let's focus on one specific type:

#📏 Vertical Asymptotes

Remember from Algebra II? Vertical asymptotes are those vertical lines that a function gets super close to but never actually touches. They're like invisible barriers! 🚧

$Graph of a function with a vertical asymptote at x = 2$

Graph of a function with a vertical asymptote at

x = 2

Key Concept

Knowing where vertical asymptotes are helps us accurately visualize functions. They represent x-values where a function's behavior is unbounded, meaning the function's value shoots up or down towards infinity.

Quick Fact

Vertical asymptotes are a type of discontinuity because the function is undefined at that specific x-value.

Exam Tip

Quick vertical asymptotes refresher: The function $f(x) = \frac{1}{x}$ has a vertical asymptote ...

#AP Calculus AB/BC: Connecting Infinite Limits and Vertical Asymptotes 🚀

Hey there! Let's dive into a crucial topic that bridges limits and discontinuities: vertical asymptotes. This is a key area, so buckle up and let's make sure you've got it down pat!

#🔗 Review: Essential Pre-requisites

Before we get started, make sure you're comfortable with these topics:

1.2: Defining Limits and Using Limit Notation
1.5: Determining Limits Using Algebraic Properties of Limits
1.6: Determining Limits Using Algebraic Manipulation

#⚠️ Understanding Discontinuities

#📏 Vertical Asymptotes

Remember from Algebra II? Vertical asymptotes are those vertical lines that a function gets super close to but never actually touches. They're like invisible barriers! 🚧

$Graph of a function with a vertical asymptote at x = 2$

Graph of a function with a vertical asymptote at

x = 2

Key Concept

Quick Fact

Vertical asymptotes are a type of discontinuity because the function is undefined at that specific x-value.

Exam Tip

Quick vertical asymptotes refresher: The function $f(x) = \frac{1}{x}$ has a vertical asymptote ...

Which of the following functions has a discontinuity at $x = 0$ ?

$g(x) = \frac{1}{x+1}$

$h(x) = \frac{1}{x}$

Which of the following functions has a discontinuity at $x = 0$ ?

$g(x) = \frac{1}{x+1}$

$h(x) = \frac{1}{x}$

Connecting Infinite Limits and Vertical Asymptotes

Abigail Young

#AP Calculus AB/BC: Connecting Infinite Limits and Vertical Asymptotes 🚀

#🔗 Review: Essential Pre-requisites

#⚠️ Understanding Discontinuities

#📏 Vertical Asymptotes

How are we doing?

Connecting Infinite Limits and Vertical Asymptotes

Abigail Young

#AP Calculus AB/BC: Connecting Infinite Limits and Vertical Asymptotes 🚀

#🔗 Review: Essential Pre-requisites

#⚠️ Understanding Discontinuities

#📏 Vertical Asymptotes

How are we doing?