Name
Student ID #
Class Section
Instructor
Math 1220
Fall 2008
EXAM
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 1220
Exam
1. Do the following problems.
(a) Dierentiate ( ) =
( )
f x
1
2
x ln
x
(b) Dierentiate ( ) = 2
f x
xsin(x)
(c) Dierentiate ( ) = 3 2
f x
x +4x
p
(d) Dierentiate ( ) = (
f x
ln
( ))
cos x
1
2. Do the following problems
(a) Use euler's method with
interval [0 1].
h
;
2
= 2 to approximate
:
y
0
=
2
x
on the
3. Integrate the following problems
R
(a)
6 + 93 + 9
2
x
f rac x
(b)
R
(c)
R
2
x
x
x
2
xdx
dx
e
x
1
dx
3
4. Do the following problems
(a) Solve the following dierential equation ( + 1) 0 =
x
y
2
x
1
y
.
(b) Suppose that tank 1 intially contains 100 gallons of solution, with
50 pounds of dissolved salt, and tank 2 contains 200 gallons, with
150 pounds of dissolved salt. Pure water ows into tank 1 at 2
gallons a minute, the well mixed solution ows out and into tank
2 at the same rate, and nally the solution in tank 2 drains away
at the same rate. Let ( ) aand ( ) denote the amount of salt in
tank 1 and 2 respectively at time t. Find ( ).
x t
y t
y t
4
5. Do the following problems.
(a) A population is growing at a rate proportional to it's size. After 5 years the population size was 164,000. After 12 years the
population size was 235,000. What was the orginal population
size?
(b) An object is taken from an oven at 300 degrees F and left to coll
in a room at 75F. If the temperature fell to 200F in half an hour
what will the tempurature be after 3 hours?
5