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Math 270 Test 5
Name ____________________
Read and follow all instructions.
Try to answer every question; remember, a partially
right answer is better than no answer at all.
Reduce all fractions to lowest terms and
round to three places past the decimal where necessary.
1. Evaluate the following limits.
a)
3
lim
x
x
x e

→∞
b)
2
0
lim
sin
x
x
x
→
2. A particle has position parameterized by
( )
24 12 , ( )
3 5
x t
t y t
t
=

= 
.
a) How fast is the particle moving?
b) Write the line as
y = mx + b
.
c) Give a different parameterization of the line with the particle starting at the same point
at
t
= 0 but moving twice as fast.
3. Parameterize each of the following curves.
a)
b)
4. Give upper and lower bounds for the following integrals using n = 50 subintervals.
a)
(
29
10
2
7
2
t
dt

∫
b)
1
2
1
1
x
e
dx
+

∫
5.
5
0
( )
4
f x dx
=
∫
and
5
0
( )
2
g x dx
= 
∫
.
Find the following integrals.
a)
5
5
( )
f x dx

∫
with
f(x)
odd.
b)
3
3
( )
g x dx

∫
with
g(x)
even
c)
0
5
3 ( )
f x dx
∫
d)
(
29
5
0
2 ( ) 5 ( )
f x
g x dx

∫
6. A termite mound’s height is a function of its age in months.
The rate of growth of a
mound is given in the following table.
Age (months)
0
3
6
9
12
15
18
Growth rate (in/month)
4
8
12
15
20
30
31
a) Approximately how tall is the termite mound when it is a year and a half old?
b) Suppose a tree is growing near the termite mound at a constant rate of fourteen inches
per month.
If the termite mound and the tree are the same age, which is taller after a year
and a half?
By how much?
3
1
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View Full DocumentMath 270 Test 5
7. The graph to the right shows the rate of change of a
company’s profits in dollars per week as a function of the
time in weeks.
At time
t=0
, the company was $50 in
debt.
What was their total profit eighteen weeks later?
8. Many elementary schools today give multiplication
speed tests to third and fourth graders to make sure students are learning the times tables.
Jesse can work problems ata rate of
9
t
problems per minute where t is in minutes.
The
test has 200 problems, so almost no one ever finishes.
Jesse’s grade is based on the
number of problems he doesn’t complete.
How many problems does Jesse have left
uncompleted if he is only allowed 10 minutes for the test?
9. A MATH 250 instructor uses chalk a a rate of
c(t)
boxes of chalk per day where t is the
number of days since the beginning of the semester.
Interpret
20
4
( )
c t dt
∫
.
10.
1600ln(
1)
C
+
computes the XP (eXperience Points) required to level up where C is
the character’s level.
a) How many XP does a level 5 character need to level up?
A level 10 character?
b) On average, how many XP per level does a character between levels 5 and 10 need to
level up?
11. Use the graph to the right to find the following
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 Summer '08
 VAKARIETIS
 Math, Fractions, Derivative, Limit, Englishlanguage films, dx

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