FORM A
Math 2214 Common Part of Final Exam Fall 2003
Instruction: Please enter your NAME, ID NUMBER, FORM designation, and CRN
NUMBER on your op-scan sheet. The CRN NUMBER should be written in the upper
right-hand box labeled “Course”. Do not include the course number. In the box labeled
“Form”, write the appropriate test form letter A. Darken the appropriate circles below
your ID number and Form designation. Use a #2 pencil; machine grading may ignore
faintly marked circles.
Mark your answers to the test question in row 1-12 of the op-scan sheet. You
have 1 hour to complete this part of the final exam. Your score on this part of the final
exam will be the number of correct answers. Please turn in your op-scan sheet and the
question sheet at the end of this part of the final exam.
1. Consider the initial value problem tan( ) ln( ), (2) 1ytyty
′
+
==. Find the largest
interval in which a solution is guaranteed to exist.
(a) ( (b) ( (c) (1, 2) 0,1) / 2,3 / 2)
π
π
(d) (1,3 / 2)
π
2. Let A be a constant matrix such that
(2 2)×48
12
A
−
=
−
and 12
24
A
=
. One
possible solution of the system A
′
=
yy
is:
(a) (b) (c)
22
2
4
2
tt
t
ee
ee
−
−
+
+
2tt
22
22
212
43
tt
t
ee
ee
−
−
+
+
2
2
2
t
t
e
e−
(d)
22
22
28
42
tt
tt
ete
ete
−
−
3. Let solve the initial value problem
( )
yt 2 , (0) 1yy t y
′
=
=. What is the value ? (2)y
(a)
y= (b) y (c) y
(2) 3 (2) 5=2
(2) e
=
(d) ye
2
(2) 2=
4. A tank initially contains 1000 gal of water in which is dissolved 20 lb of salt. A valve
is opened at time t = 0 and water containing 0.2 lb of salt per gallon flows into the
tank at a rate of 5 gal/min. The mixture in the tank is well stirred and drains from the
tank at the same rate of 5 gal/min. Determine the time t, in minutes, that the tank
contains 180 lb of salt.
(a) te (b) te (c) t
180/ 200
=200/ 180
=200 ln 9
=
(d) tln(180/ 200)
=
