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13 Solved Problems on the Differential Equations - Exam 1 | MTH 252, Exams of Calculus

Material Type: Exam; Class: Calculus II; Subject: Math; University: Portland Community College; Term: Winter 2006;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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MTH 252 - Winter Term 2006
Test 2 No Calc Portion Name
1. Find each the following general antiderivatives. No work (other than the answer) should be
shown. (14 points total)
a.
5t
edt=
b.
() ()
sec tan
x
xdx=
c.
2
dx
x
=
d.
()
7
8tdt=
e.
cos 5d
α
α
⎛⎞ =
⎜⎟
⎝⎠
f.
2
2
x
x
edx=
g.
(
)
2
sec
d
θ
θ
=
h.
2
8
x
dx
x
=
3/2/2006 7:03PM
1 / 9
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Download 13 Solved Problems on the Differential Equations - Exam 1 | MTH 252 and more Exams Calculus in PDF only on Docsity!

MTH 252 - Winter Term 2006

Test 2 – No Calc Portion Name

  1. Find each the following general antiderivatives. No work (other than the answer) should be

shown. (14 points total)

a.

5 t

e dt =

b. sec ( x ) tan( x dx ) =

c.

dx

x

d. ( )

7

8 t dt =

e. cos

d

f.

2

x

x e dx =

g. ( )

2

sec θ d θ =

h. 2

8 x dx

x

MTH 252 Test 2 Key

  1. Find the solution to the differential equation

dy x 1

dx (^) x

= where y ( 1 ) = 0. (6 points total)

  1. Evaluate

( )

3

1 1

dx

x x +

after making the substitution u = x. (6 points)

MTH 252 Test 2 Key

b. Evaluate

1

0 4

4 3

x

dx

x

. (6 points)

c. Evaluate ( )

2

x ln x dx

. (5 points)

MTH 252 Test 2 Key

  1. Fill in each blank based upon Figure 6. No work

need be, nor should be, shown. (2 points each)

a. A =

b. B =

c. (^) ( )

4

0

f x dx = ∫

d. (^) ( )

4

2

f x dx = ∫

e. (^) ( )

2

0

f x dx = ∫

f. (^) ( )

4

0

f ′^ x dx = ∫

g. ( )

4

0

f ′′^ x dx = ∫

  1. Suppose that Criminy Cricket was bouncing up and down. Suppose further that h t ( (^) )was Mr.

Cricket’s height above the ground t seconds after noon and that exactly at noon the little

bugger was moving upward at 12 cm/s. Finally, suppose that the acceleration function for this

little escapade was that shown in Figure 7. When, over the first 10 seconds after noon, was Mr.

Cricket moving most rapidly? Please be sure that you clearly explain the reasoning you used to

determine your answer. (5 points)

Figure 6

y = f (^) ( x )

A

B

x

y

y (cm/s/s)

t (s)

Figure 7

y = h ′′ ( t )

MTH 252 Test 2 Key

  1. Suppose that (^) ( )

2

4

x

F x = t + dt

. (3 points each)

a. What is the value of F ′^ ( 4 )?

b. Is F (^) ( 0 )positive or is F (^) ( 0 )negative? Explain how you know.

  1. If h ′ (^) ( t )is the rate of change in a child’s height measured in inches per year, what does the

integral (^) ( )

10

0

ht dt

represent and what are its units? (4 points)

MTH 252 Test 2 Key

  1. If H ( ) t is the rate of change in the speed of sound with respect to temperature measured in

ft/s per

Ο F, what does the integral (^) ( )

100

32

H t dt

represent and what are its units? (4 points)

  1. Evaluate

4

0

j

j =

. (3 points)

Extra Credit

Evaluate

( )

100

2 2

1

k 1

k = k

. Make sure that your reasoning is clear.