Name:
Instructor:
Math 10550, Practice Exam III
November 20, 2024
• The Honor Code is in e↵ect for this examination. All work is to be your own.
• No calculators.
• The exam lasts for 1 hour and 15 min.
• Be sure that your name is on every page in case pages become detached.
• Be sure that you have all 12 pages of the test.
• Each multiple choice question is worth 7 points. Your score will be the sum of the best
10 scores on the multiple choice questions plus your score on questions 13-15.
PLEASE MARK YOUR ANSWERS WITH AN X, not a circle!
1. (a) (b) (c) (d) (e)
2. (a) (b) (c) (d) (e)
........................................................................................................................
3. (a) (b) (c) (d) (e)
4. (a) (b) (c) (d) (e)
........................................................................................................................
5. (a) (b) (c) (d) (e)
6. (a) (b) (c) (d) (e)
........................................................................................................................
7. (a) (b) (c) (d) (e)
8. (a) (b) (c) (d) (e)
........................................................................................................................
9. (a) (b) (c) (d) (e)
10. (a) (b) (c) (d) (e)
........................................................................................................................
11. (a) (b) (c) (d) (e)
12. (a) (b) (c) (d) (e)
Please do NOT write in this box.
Multiple Choice
13.
14.
15.
Total
Name:
Instructor:
Multiple Choice
x4 x3
1.(7 pts.) How many inflection points does the curve y = have?
12 3
(a) 1 (b) 3 (c) 2 (d) 4 (e) 0
3x3 2x + 1
2.(7 pts.) Evaluate lim
x! 1 2x2 + x + 1
3 3
(a) 0 (b) (c)
2 2
(d) 1 (e) Does not exist
2
Name:
Instructor:
2x4 + x3 + 5
3.(7 pts.) The slant asymptote of y = is given by
x3 3x2 + 2
(a) There are no slant asymptotes. (b) y = 2x + 7
(c) y =x+4 (d) y = 2x 5
(e) y = 2x + 4
p
4x6 + 5
4.(7 pts.) Evaluate lim .
x! 1 x3 + 1
(a) 3/2 (b) 6 (c) 2 (d) 2 (e) 4
3
Name:
Instructor:
5.(7 pts.) If we want to use Newton’s method to find an approximate solution to
cos(x) x = 0
⇡
with initial approximation x1 = , what is x2 ?
2
3⇡ ⇡ ⇡
(a) (b) 0 (c) (d) ⇡ (e)
4 2 4
6.(7 pts.) A bug being chased by a kitten (both moving in a straight line) enters a
2
kitchen with velocity 1 ft/sec, and accelerates at p ft/sec2 . How fast is the bug moving
t
9 seconds later.
(a) 13 ft/sec (b) 7 ft/sec (c) 5 ft/sec
(d) 4 ft/sec (e) 37 ft/sec
4
Name:
Instructor:
7.(7 pts.) Find the left endpoint approximation to the definite integral
Z 3
6
dx
1 2+x
using four approximating rectangles of equal base width.
71 131 71 25
(a) (b) (c) 25 (d) (e)
10 10 5 2
8.(7 pts.) If f (x) is a continuous function with
Z 1 Z 2 Z 5
f (x) dx = 2, f (x) dx = 1 and f (x) dx = 2
2 2 2
Z 5
find f (x) dx.
1
(a) 2 (b) 3 (c) 0 (d) 1 (e) 6
5
Name:
Instructor:
9.(7 pts.) Calculate the following definite integral
Z 3p
x + x3
dx.
1 x5/2
3 p
(a) (b) 2 3
2
5 p 1
(c) (d) 2 3
2 3
p 1
(e) 2 3+
2
6
Name:
Instructor:
10.(7 pts.) The graph shown below is that of f (x) for 1 x 4 where
8
>
<2p if 1 x 0
f (x) = 4 x2 if0 < x 2
>
:4 2x if2 x 4
Z 4
Which of the following equals f (x)dx?
1
y = f(x)
-1 1 2 3 4
-1
-2
-3
-4
(a) ⇡ 2 (b) ⇡ (c) 6+⇡
(d) 2⇡ 2 (e) 0
7
Name:
Instructor:
Z 1 p
11.(7 pts.) If f (x) = 1 + sin(t) dt, then f 0 (x) =
x3
p p p
(a) 1 + sin(x3 ) (b) 1 + sin(x) (c) 1 + sin(x3 )
p p
(d) 3x2 1 + sin(x3 ) (e) 3x2 1 + sin(x3 )
8
Name:
Instructor:
12.(7 pts.) The graph of f (x) is shown below:
y = f(x)
y
x
-4 -3 -2 -1 1 2 3 4
which of the following gives the graph of an antiderivative for the function f (x)?
y y
x
-4 -3 -2 -1 1 2 3 4
(a) (b) x
-4 -3 -2 -1 1 2 3 4
y y
(c) (d)
x
-4 -3 -2 -1 1 2 3 4
x
-4 -3 -2 -1 1 2 3 4
(e)
x
-4 -3 -2 -1 1 2 3 4
9
Name:
Instructor:
Partial Credit
You must show your work on the partial credit problems to receive credit!
13.(10 pts.) A page of a book is to have a total area of 150 square inches, with 1 inch
margins at the top and sides, and a 2 inch margin at the bottom. Find the dimensions
in inches of the page which will have the largest print area.
10
Name:
Instructor:
14.(10 pts.) A particle is moving in a straight line with acceleration
✓ ◆
2 1
a(t) = 4 t ft/s2 ,
3
where distance is measured in feet and time in seconds. The initial velocity of the particle
is v(0) = 0 ft/s and the initial position of the particle is s(0) = 0.
(a) Find the velocity of the particle at time t (i.e. find v(t)).
(b) Find the position of the particle at time t (i.e. find s(t)).
(c) Find the values of t for which v(t) = 0 on the interval [0, 1).
(d) Find the distance travelled by the particle on the time interval 0 t 2.
11
Name:
Instructor:
15.(10 pts.) Evaluate the definite integral shown below using right endpoint approxi-
mations and the limit definition of the definite integral
Z 2
x
dx
0 2
n
!
X n(n + 1)
Note: 1 + 2 + 3 + · · · + n = i= .
i=1
2
Verify your answer using the fundamental theorem of calculus.
12
Name:
Instructor: ANSWERS
Math 10550, Practice Exam III
November 20, 2024
• The Honor Code is in e↵ect for this examination. All work is to be your own.
• No calculators.
• The exam lasts for 1 hour and 15 min.
• Be sure that your name is on every page in case pages become detached.
• Be sure that you have all 12 pages of the test.
• Each multiple choice question is worth 7 points. Your score will be the sum of the best
10 scores on the multiple choice questions plus your score on questions 13-15.
PLEASE MARK YOUR ANSWERS WITH AN X, not a circle!
1. (a) (b) (•) (d) (e)
2. (a) (b) (c) (•) (e)
........................................................................................................................
3. (a) (•) (c) (d) (e)
4. (a) (b) (•) (d) (e)
........................................................................................................................
5. (a) (b) (c) (d) (•)
6. (•) (b) (c) (d) (e)
........................................................................................................................
7. (a) (b) (c) (d) (•)
8. (a) (b) (c) (•) (e)
........................................................................................................................
9. (a) (•) (c) (d) (e)
10. (•) (b) (c) (d) (e)
........................................................................................................................
11. (a) (b) (c) (•) (e)
12. (a) (•) (c) (d) (e)
Please do NOT write in this box.
Multiple Choice
13.
14.
15.
Total
