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# Section 1.2 - Finding Limits Graphically and Numerically - PowerPoint PPT Presentation

Section 1.2 - Finding Limits Graphically and Numerically. Limit. Informal Definition: If f ( x ) becomes arbitrarily close to a single REAL number L as x approaches c from either side, the limit of f ( x ) , as x appraches c , is L. f ( x ). L. x. c. The limit of f(x)….

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### Section 1.2 - Finding Limits Graphically and Numerically

Informal Definition: If f(x) becomes arbitrarily close to a single REAL number L as x approaches c from either side, the limit of f(x), as x appraches c, is L.

f(x)

L

x

c

The limit of f(x)…

is L.

Notation:

as x approaches c…

Our book focuses on three ways:

Numerical Approach – Construct a table of values

Graphical Approach – Draw a graph

Analytic Approach – Use Algebra or calculus

This Lesson

Next Lesson

Use the graph and complete the table to find the limit (if it exists).

6.859

7.88

7.988

8

8.012

8.12

9.261

If the function is continuous at the value of x, the limit is easy to calculate.

Use the graph and complete the table to find the limit (if it exists).

Can’t divide by 0

-2.1

-2.01

-2.001

DNE

-1.999

-1.99

-1.9

If the function is not continuous at the value of x, a graph and table can be very useful.

Use the graph and complete the table to find the limit (if it exists).

-6

2.9

2.99

-6

2.999

8

2.999

2.99

2.9

If the function is not continuous at the value of x, the important thing is what the output gets closer to as x approaches the value.

The limit does not change if the value at -4 changes.

f(x)approaches a different number from the right side of c than it approaches from the left side.

f(x)increases or decreases without bound as x approaches c.

f(x)oscillates between two fixed values as x approaches c.

Closest

Closer

Close

If the domain is restricted (not infinite), the limit off(x)exists as x approaches an endpoint of the domain.

Given the function t defined by the graph, find the limits at right.

Sketch a graph of the function with the following characteristics:

• does not exist, Domain: [-2,3), and Range: (1,5)

• does not exist, Domain: (-∞,-4)U(-4,∞), and Range: (-∞,∞)

Sketch a graph and complete the table to find the limit (if it exists).

2.8680

2.732

2.7196

DNE

2.7169

2.7048

2.5937

This a very important value that we will investigate more in Chapter 5. It deals with natural logs.

Why is there a lot of “noise” over here?