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6 Problems in Exam for Calculus II | MTH 252, Exams of Calculus

Material Type: Exam; Class: Calculus II; Subject: Math; University: Portland Community College; Term: Winter 2009;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Your documentation will be graded along with the “correctness” of your solution. Page 1 of 6
MTH 252 – Test 3 – Take home portion
Distributed March 12, 2009 Name
Due: 6:00 PM, March 19, 2009
Work each of these problems entirely by yourself.
Do not get help from any person on any of these questions.
Do not get help from any person on any question that is essentially the same as any of these
questions.
Do not compare your answers or work with any other person’s answers or work.
Do not have any other person look over your work or check your answer.
You may look at your notes and textbook while working these problems. Remember, though, that
there will be questions like these on your final exam and you will not have notes or a textbook to
look at while taking your final exam. The exception to the later statement is that your final will
include area questions rather than volume questions.
1. A force of 0.6 N is required to hold a spring whose natural length is 62 cm at a length of 72 cm.
How much work is done when stretching the spring from its natural length to a length of 72 cm?
Note: A Newton-
meter
is called a Joule (J); make sure that you include units while making your
calculations and that you state your conclusion using the unit of Joule.
pf3
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MTH 252 – Test 3 – Take home portion

Distributed March 12, 2009 Name

Due: 6:00 PM, March 19, 2009

Work each of these problems entirely by yourself.

Do not get help from any person on any of these questions.

Do not get help from any person on any question that is essentially the same as any of these questions.

Do not compare your answers or work with any other person’s answers or work.

Do not have any other person look over your work or check your answer.

You may look at your notes and textbook while working these problems. Remember, though, that there will be questions like these on your final exam and you will not have notes or a textbook to look at while taking your final exam. The exception to the later statement is that your final will include area questions rather than volume questions.

  1. A force of 0.6 N is required to hold a spring whose natural length is 62 cm at a length of 72 cm. How much work is done when stretching the spring from its natural length to a length of 72 cm?

Note: A Newton- meter is called a Joule (J); make sure that you include units while making your

calculations and that you state your conclusion using the unit of Joule.

  1. The boundary curves of the region outlined in Figure 1 are sin (^) ( 1 ) 4

x y

⎛ π ⎞

and

5 cos 1

y

x

⎛ π ⎞

. Find the volume of the solid that results from revolving the outlined

region about the line x = − 6. Remember to include all of the labels and work discussed and

illustrated in class.

Figure 1

4. A graph of the function ( )

f x

x

= is shown in Figure 3. Suppose that the region between

y

x

= and the x -axis over the interval [ 1, t ]were rotated about the x -axis. Suppose further

that t → ∞.

Write down the disk method inspired improper integral that would compute the resultant solid’s volume and then write down the improper integral that would compute the solid’s surface area.

Evaluate each integral on your calculator and write down the somewhat surprising results. In

case you haven’t yet discovered this, you’re calculator will accept ∞ as an integral limit.

You do not need to include fancy labels on this problem – just give me the integrals and answer.

Surface area integral: ( ) ( )

2

b

a^ π^ f^ x^ f^ x^ dx

∫ + ⎡⎣^ ′ ⎤⎦

Figure 3

5. A function g is shown in Figure 4; the portions of

the curve that look quarter-circular are indeed

quarter-circular. Find the average value of g over

[1,8 ]^. Make sure that your reasoning is clear.

Figure 4