MATH 1352-008
Exam I
September 24, 1998
Answer the problems on separate paper. You do not need to rewrite the problem
statements on your answer sheets. Do your own work. Show all relevant steps
which lead to your solutions. Retain this question sheet for your records.
1. Match the following functions with their graphs:
i) y ' ln ( x % 1 )
x
iii) y '
x%1
a) Graph A
c) Graph C
ii) y ' 2 &x & 1
iv) y ' 2 x & 1
b) Graph B
d) Graph D
2.
Find the absolute maximum and minimum of y ' 4 x 2 e &x
3.
Find y ) for
(a) y '
4.
1 % t 2 ln t
t2
on [0,3].
e &t
( sin t & cos t )
2
ln 9
(b)
m
e &x/2 dx
ln 4
Evaluate the following limits
(a) lim
x60
6.
/2
Evaluate the following integrals
dx
(a)
m x % x ln ( 2 x )
5.
(b) y '
2
x2
ln ( sec x )
(b) lim (
x60
1
1
&
)
x ln ( x % 1 )
The half-life of radon-222 is 3.85 days. If after a week, the strength of the
sample (the measured level of radioactive decay per unit mass) is 4.5
hundred thousand neutrons per second, what was the initial strength of the
sample?