Name: 
 

04-07-Numerical Integration and Basic Differntial Equations



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

 1. 

Given  mc001-1.jpg  and  mc001-2.jpg  which statement correctly describes mc001-3.jpg?

 

a.
mc001-4.jpg
e.
mc001-8.jpg
b.
mc001-5.jpg
f.
mc001-9.jpg
c.
mc001-6.jpg
g.
mc001-10.jpg
d.
mc001-7.jpg
h.
mc001-11.jpg
 

 2. 

An airplane is left Los Angeles at 12 noon and is flying to Atlanta. If the plane traveled 340 miles after 1 hour and for the next few hours the velocity of the plane can be described by the function, mc002-1.jpg where x represents the number of hours after 12 noon.  Which function describes the distance traveled by the airplane t hours after 12 noon
(at least for as long as the velocity function holds true)?

 



mc002-2.jpg

a.

mc002-3.jpg

 


c.

mc002-5.jpg

 


b.

mc002-4.jpg


d.
mc002-6.jpg
 

 3. 

Rewrite mc003-1.jpg using an approximating Rieman Sum with n = 99.


a.

mc003-2.jpg

 


b.

mc003-3.jpg

 


c.

mc003-4.jpg

 


d.

mc003-5.jpg

 


e.

mc003-6.jpg

 

 

 4. 

Consider  mc004-1.jpg. If a Reimann Sum were to be created to approximate mc004-2.jpg, what would the most appropriate equation to describe mc004-3.jpg
with n =40?


a.
mc004-4.jpg
b.
mc004-5.jpg
c.
mc004-6.jpg
d.
mc004-7.jpg
 

 5. 

Consider  mc005-1.jpg. If a Reimann Sum were to be created to approximate mc005-2.jpg, what would the most appropriate equation to describe mc005-3.jpg with n =50  using right-hand endpoints?


a.
mc005-4.jpg
b.
mc005-5.jpg
c.
mc005-6.jpg
d.
mc005-7.jpg
 

 6. 

Given,  mc006-1.jpg.  What would be the approximation of  mc006-2.jpg using an approximating Rieman Sum with n = 56 and right hand endpoints.

Use a TI-84 or spreadsheet to assist.



a.
mc006-3.jpg
b.
mc006-4.jpg
c.
mc006-5.jpg
d.
mc006-6.jpg
 

 7. 

Use your TI-84 or a spreadsheet to evaluate:

mc007-1.jpg

a.
mc007-2.jpg
b.
mc007-3.jpg
c.
mc007-4.jpg
d.
mc007-5.jpg
 

 8. 

Consider the derivative:

mc008-1.jpg

with the initial condition:

mc008-2.jpg

A student graphed each consecutive estimate of mc008-3.jpg using Euler’s Method.  What did the student use for mc008-4.jpg?

 

 

 

mc008-5.jpg

a.
mc008-6.jpg
c.
mc008-8.jpg
b.
mc008-7.jpg
d.
mc008-9.jpg
 

 9. 

Consider the derivative:

mc009-1.jpg

with the initial condition:

mc009-2.jpg

Using Euler’s Method with mc009-3.jpg approximate mc009-4.jpg



a.
mc009-5.jpg
c.
mc009-7.jpg
b.
mc009-6.jpg
d.
mc009-8.jpg
 

 10. 

Consider the derivative:

mc010-1.jpg

with the initial condition:

mc010-2.jpg

Using Euler’s Method with mc010-3.jpg approximate mc010-4.jpg.



a.
mc010-5.jpg
c.
mc010-7.jpg
b.
mc010-6.jpg
d.
mc010-8.jpg
 



 
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