MATH 152, Exam I, Version B
Fall, 1994
NAME
ID #
INSTRUCTOR'S NAME
SECTION #
INSTRUCTIONS
1. In Part I (problems 1-10), mark the correct choice on your SCANTRON sheet using
a #2 pencil. For your own records, record your responses on your exam (which will
be returned to you). The SCANTRON will be collected after 1 hour and will not be
returned.
2. In Part II (problems 11-20), write all solutions in the space provided. Use the back
of each page for scratch work, but all work to be graded must be shown in the space
provided. CLEARLY INDICATE YOUR FINAL ANSWER.
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MATH 152, Exam I, Version B
Part I. MULTIPLE CHOICE, NO PART CREDIT, NO CALCULATORS
The SCANTRON forms will be collected at the end of 1 hour.
1. Evaluate
Z
ex dx
1 + ex
(B) ln(3)
(c) ln(1 + ln 5)
ln(5)
0
(a) 4 ln(3)
2. Evaluate
Z
ln(2)
0
(a) 1
and
a
(a) ln(a b) = ln(a) + ln(b)
(D) 23
(c) 2
b
4. Evaluate
1
(A) 15
5. Find
(a) 1
=4
0
1
(e) ln(a) ln(b) = ln
a
b
sin2 (2) cos3(2) d.
4
(b) 15
dy
dx
(e) e
are positive real numbers, which of the following is FALSE?
p
(b) aln(b) = bln(a)
(c) ln( a) = 12 ln(a)
a
a)
(D) ln(
=
ln
ln(b)
b
Z
(e) ln(5) ln(1 + ln 5)
e2x dx.
(b) e2
3. Given that
(d) ln(5)
3
5
(d) 96
(c) 1
2560
3
(e) 384
5
10240
at (1; e) if (x + y) ln y = 1 + e.
(b) 0
(C) 1 +e2e
(d) 1 +e 2e
2
(e) 1 e 2e
(1 cos t) sin t .
6. Evaluate tlim
!0
t3
(c) 1
(a) 0
(B) 21
7. Evaluate
(a) 3e13
Z
1
0
1
e
e
2x
(d) 12
(e) sinh x dx.
1
(b) 6e13 2e
(d) 3e13 1e 23
2 sinh(1) + 1
(c) cosh(1)
2
5e
5e2
2
1 +1
(E) 6e13 2e
3
cos 1 (2x) = arccos(2x), then f 0(x) =
(b) p 1 2
(C) p 2 2
(d) p 22
(a) p 12
4x 1
1 4x
1 4x
4x 1
8. If
f (x) =
9. Evaluate
Z
(a) sin(3x) + C
(e) p 2 2
1 4x
3x cos(3x) dx.
(b) 13 x cos(3x) + 19 cos(3x) + C
(d) x cos(3x) sin(3x) + C
(c) x sin(3x) 91 cos(3x) + C
(E) x sin(3x) + 13 cos(3x) + C
10. y = 12 sin(2 arctan x) has the same graph as
(A) y = 1 +x x2
p
(b) y = 1 + x2
(d) y = p 1 2
2 1+x
3
(c) y = p
(e) y = 1 +1 x2
x
1 + x2
Part II. WORK OUT PROBLEMS, PART CREDIT will be given.
CALCULATORS ARE PERMITTED after the SCANTRONS are collected.
Show all relevant steps in your solution. Clearly indicated your answer. Unsupported
answers will not be given credit. Only work shown in the space provided will be graded.
11. Use the Trapezoidal Rule to approximate
the area of the lake behind the dam pictured at
the right. The measurements are in hundreds of
meters, made at intervals 50 meters apart.
12. An advertiser wants to place a billboard
at some distance x from where viewers will
stand at P . (See gure.) What choice of x
will maximize the viewing angle ? All distances are in feet. Hint: Use inverse trig functions to express as a function of x.
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13. Find the partial fraction decomposition of
14. Evaluate
Z
x3
x2 + 2
.
x2 x
1 dx.
+x
15. Find the area of the region bounded by the x-axis, the graph of
the lines x = 1 and x = 2.
5
y
= xe x , and
16. The temperature of a cup of coee as it is poured by a waiter is 180 F. The room
temperature is 70 F. Three minutes later, the cup of coee has cooled to 140 F.
The temperature T ( F ) of the cup of coee can be modelled by Newton's Law of Cool= k(T 70). The solution to this dierential equation is T = 70 + C ekt .
ing as dT
dt
If the customer prefers coee at 120 F, how much time should she wait after it is
poured before drinking it?
17. Let f (x) = e5x + 3e2x + 2
a) Compute f (0).
b) Explain why
f
has an inverse function for all x.
c) Find the derivative of the inverse function at 6, i.e., nd (f 1)0(6).
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18. Evaluate
Z
3=2
0
px
9
2
x2
dx.
Zx
2
19. Evaluate xlim
!1 x ln x 1 ln t dt.
2
20. Compute xlim
1
!1
x
x
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