Name
Student ID #
Class Section
Instructor
Math 1100
Fall 2006
EXAM I
Dept. Use Only
Exam Scores
Problem Points Score
1.
20
2.
20
3.
20
4.
20
5.
20
TOTAL
Show all your work and make sure you justify all your
answers.
Math 1100
practice Exam
dy
for three of the four problems below. (If you do not clearly
1. Find dx
indicate which two you want graded I reserve the right to give you a
zero score.)
(a) = x7 x ( )
y
+
e
2
ln x
(b) = ( ( + 1)) +
e
3
y
3
ln ln x
(c)
y
ln xy
(d)
2
ln x y
2
ex +1
( ) + ( + 1)
(
2
x
e
+ ) + ( + 1)
x
y
2
3
.
y2 +1
x2 +1
e
1
x
+ 10 = 0
) 10 + 10 = 0
x
2. Integrate three of the four problems below. (If you do not clearly
indicate which two you want graded I reserve the right to give you a
zero score.)
R
(a) ( + 1) x4 x
3
(b)
R
(c)
R
(d)
R
x
e
(
1) 12
x x
3
x2
3
+4 +4
dx
(x +4)ln(x +4)
1
1+e
dx
dx
3x dx
2
3. Find the denite integral for two of the three problems below. (If you
do not clearly indicate which two you want graded I reserve the right
to give you a zero score.)
(a)
R5
(b)
R5
(b)
R5
x2
x3 +4 dx
1
0
j
x
x5
2j
dx
x5 dx
(Hint show this is an odd function. What do you
know about an odd function on a symmtric interval?) Justify your
answer.
5
e
e
3
4. Answer one of the two problems below. (If you do not clearly indicate
which two you want graded I reserve the right to give you a zero score.)
(a) Find consumer and producer surplus given demand function ( ) =
+ 10 and supply function ( ) = 1 + 2.
D x
x
2
S x
: x
(b) Find the area bounded by the curves ( ) = 3
( )=
+2
f x
g x
x
2
x
4
3
x
2
x
10 and
x
5. Given that your marginal cost is 50 8 and marginal revenue is
10 + 50 nd your prot function given that when you produce no
units you make no prot. Find how much prot you make when you
produce ten units by expressing this as a denite integral (what does
the denite integral represent?).
: x
x
5