   Chapter 9.1, Problem 14E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 11-14, complete each table and predict the limit, if it exists. f ( x ) { 4 − x 2 for  x ≤ − 2 x 2 + 2 x for  x > − 2 lim x → − 2 f ( x ) = ? x f (x) -2.1 -2.01 -2.001 -1.999 -1.99

To determine

The following table and predict if the limit limx2f(x) exists,

 x f(x) −2.1 −2.01 −2.001 −1.999 −1.99
Explanation

Given Information:

The function is f(x)={4x2           for x2x2+2x         for x>2.

The incomplete table

 x f(x) −2.1 −2.01 −2.001 −1.999 −1.99

Explanation:

Consider the provided function,

f(x)={4x2           for x2x2+2x         for x>2 …… (1)

Consider the provided, incomplete table,

 x f(x) −2.1 −2.01 −2.001 −1.999 −1.99

For x=2.1, substitute 2.1 for x in the function (1),

f(2.1)=4(2.1)2=44.41=0.41

For x=2.01, substitute 2.01 for x in the function (1),

f(2.01)=4(2.01)2=44.0401=0.0401

For x=2.001, substitute 2.001 for x in the function (1),

f(2.001)=4(2.001)2=44.0040=0.0040

For x=1.999, substitute 1.999 for x in the function (1),

f(1.999)=(1.999)2+2(1.999)=3

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