Name: 
 

03-05 - Linear Approximations



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

Use the linear approximation (i.e. tangent line) of the function mc001-1.jpg at  mc001-2.jpg  to approximate the number mc001-3.jpg.
a.
2.99
d.
3.03
b.
mc001-4.jpg
e.
3.04
c.
3.02
 

 2. 

Let f  be the function given by mc002-1.jpg.  What approximation would be given for mc002-2.jpg using the line tangent to the graph of f  at mc002-3.jpg?
a.
mc002-4.jpg
d.
mc002-7.jpg
b.
mc002-5.jpg
e.
mc002-8.jpg
c.
mc002-6.jpg
f.
mc002-9.jpg
 

 3. 

The function f  is twice differentiable with mc003-1.jpgmc003-2.jpgmc003-3.jpg.  What is the value of the approximation of mc003-4.jpg using the tangent of f  at x = a?
a.
mc003-5.jpg
d.
mc003-8.jpg
b.
mc003-6.jpg
e.
mc003-9.jpg
c.
mc003-7.jpg
f.
Not Enough Information Provided
 

 4. 

Using differentials:
Given the equation  mc004-1.jpg

What would be the approximation of  mc004-2.jpg using differentials?
(let x = 4 and mc004-3.jpg)

a.
mc004-4.jpg
d.
mc004-7.jpg
b.
mc004-5.jpg
e.
mc004-8.jpg
c.
mc004-6.jpg
f.
Not enough information
 

 5. 

Given the function  mc005-1.jpg and the following information:

•  mc005-2.jpg•  dx = 0.2 mc005-3.jpg

Using differentials, what would be the best approximation of mc005-4.jpg?
a.
mc005-5.jpg
d.
mc005-8.jpg
b.
mc005-6.jpg
e.
mc005-9.jpg
c.
mc005-7.jpg
f.
mc005-10.jpg
 

 6. 

Given the function  mc006-1.jpg and the following information:

mc006-2.jpg
mc006-3.jpg

Using differentials, what would be the best approximation of  mc006-4.jpg?
a.
mc006-5.jpg
d.
mc006-8.jpg
b.
mc006-6.jpg
e.
mc006-9.jpg
c.
mc006-7.jpg
f.
mc006-10.jpg
 



 
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