Name
Student ID #
Math 1320
Spring 2014
SAMPLE EXAM I
This is only to give you a general idea of what to expect. The actual exam
may or may not include problems similar to those given here, and it may be
longer or shorter.
Instructions: Show all of your work for full credit.
Problem
1.
2.
3.
4.
5.
Points
20
20
20
20
20
TOTAL
Score
(20 points) 1. Find the volume of the solid obtained by rotating the region bounded
by the curves x = cos y, y = 0, y = π/2, about the x-axis.
(20 points) 2. Find the work required to lift a 500 lb container of drywall from ground
level to the top floor at 400 ft. The container is pulled by a cable which
weighs 2 lb/ft.
1
(20 points) 3. (a) Solve the initial value problem
dy
2xy
= 2
, y(0) = 1.
dx
x +1
(b) Use Euler’s Method with step size 0.1 to estimate y(0.3).
2
(20 points) 4. A cup of coffee is poured at 180 ◦ F, and placed on a desk in a 70 ◦ F
room to cool. After 5 minutes, the coffee is at 140 ◦ F. How long after
pouring will it take for the coffee to reach 90 ◦ F?
(20 points) 5. Find the radius of convergence and the interval of convergence for the
∞
X
(2x − 2)n
(−1)n √
power series
.
n+1
n=0
3