   Chapter 9.1, Problem 12E ### 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 ) = 2 x + 1 1 4 − x 2 lim x → − 0.5 f ( x ) = ? X f(x) -0.51 -0.501 -0.5001 -0.4999 -0.499 -0.49

To determine

The following table and predict the limx0.5f(x), if it exists,

 x f(x) −0.51 −0.501 −0.5001 −0.4999 −0.499 −0.49
Explanation

Given Information:

The function is f(x)=2x+114x2.

The complete table is given below,

 x f(x) −0.51 −0.501 −0.5001 −0.4999 −0.499 −0.49

Explanation:

Consider the provided function,

f(x)=2x+114x2

Rewrite the function,

f(x)=2x+10.25x2

Consider the provided, incomplete table,

 x f(x) −0.51 −0.501 −0.5001 −0.4999 −0.499 −0.49

For x=0.51:

Substitute 0.51 for x in the function f(x):

f(0.51)=2(0.51)+10.25(0.51)2=1.02+10.250.2601=0.020.0101=1.9802

For x=0.501:

Substitute 0.501 for x in the function f(x):

f(0.501)=2(0.501)+10.25(0.501)2=1.002+10.250.251001=0.0020.001001=1.9980

For x=0.5001

Substitute 0.5001 for x in the function f(x):

f(0.5001)=2(0.5001)+10.25(0.5001)2=1.0002+10.250.25010001=0.00020.00010001=1.9998

For x=0.4999:

Substitute 0.4999 for x in the function f(x):

f(0.4999)=2(0.4999)+10.25(0.4999)2=0.9998+10.250.24990001=0

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