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Material Type: Exam; Class: Calculus II; Subject: Math; University: Portland Community College; Term: Winter 2006;
Typology: Exams
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MTH 252 - Winter Term 2006
Test 2 – No Calc Portion Name
shown. (14 points total)
a.
5 t
e dt =
c.
dx
x
7
8 t dt =
e. cos
d
f.
2
x
x e dx =
2
h. 2
8 x dx
x
MTH 252 Test 2 Key
dy x 1
dx (^) x
= where y ( 1 ) = 0. (6 points total)
( )
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
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 = ∫
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 )
x
y
y (cm/s/s)
t (s)
Figure 7
y = h ′′ ( t )
MTH 252 Test 2 Key
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.
integral (^) ( )
10
0
h ′ t dt ∫
represent and what are its units? (4 points)
MTH 252 Test 2 Key
ft/s per
Ο F, what does the integral (^) ( )
100
32
H t dt ∫
represent and what are its units? (4 points)
4
0
j
j =
∑
. (3 points)
Extra Credit
Evaluate
( )
100
2 2
1
k 1
k = k
∑
. Make sure that your reasoning is clear.