5.2.1 Introduction to Limits

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5.2.1 Introduction to LimitsToday you will:• Develop an intuitive

idea of limit• Interpret limit

statements written with proper notation

Sketch the graph 1 32

a. Benny starts at the point corresponding to x = 6 and moves along the graph to the left, so he’s climbing uphill. How high does Benny think he’ll get as x gets closer to 3?

Consider the graph at right when answering the questions below.

b. Benny’s sister Bertha starts at the point corresponding to x = -3 and moves to the right. How high does Bertha think she’ll get as x gets closer to 3?

Consider the graph at right when answering the questions below.

a. Suppose Bertha also starts at the point where x = 5, but she moves to the left. What is she thinking as she gets closer to x = 2? The limit statement for Bertha’s scenario is

Limits

lim 3x

b. Did you notice the ‘+’ next to the 2 in part a? What do you think it means? This is called a one-sided limit. What do you think it would mean if there were a ‘–’ sign instead?

Limits

lim 3x

c. On the graph of problem 5-42, evaluate the following limits:

Limits

lim 3x

Complete

5-44, 5-45 and 5-46with your partner.

Partner Work

Class Discussion

Limits and TablesWorking with one-sided limits

Today you will:1. Understand the necessary conditions for a limit to exist2. Practice finding limits 3. Predict limits from tables

« Intermission » CheckUse the given function f(x) shown. a. Benny Bug starts at the

point (2,2.5) and moves along the graph to the right. What does he think his height will be at x = 3?

This is the key to limits: what does Benny think his y-coordinate will be as x approaches a certain value?

« Intermission » Checkb. If Bertha starts at the point

(5,1) and moves to the left, what does she think her y-value will be as x approaches 3?

Write limit statements for Benny and Bertha Bug as they approach x = 3 from both sides.

c. Using the same function as above, complete the following limit statements:

lim _____ lim _____x x

f x f x

Limit Definition

It is important to be able to tell when a limit exists and when it does not. What condition must be met for a limit to exist? Rephrase the definition of a limit from the Math Notes above into your notes.

5-70: Partner Work

5-70 Sketch a function f(x) whose domain is all real numbers such that

3 3lim limx x

f x f x

As a Class5-71 Look at the table of values shown below for some

function f(x).

Partner Exit Slip

Please complete and turn in the exit slip before starting

on your assignment.

Partner Exit Slip5-69 The graph of f(x) is shown to the right.

AssignmentHW 5.2.1

5-47 to 5-54And 5-58, 5-59, 5-

61, 5-62See yu

tmrrw!

5.2.1 Introduction to Limits

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