x
y
x
1800W081
MAT 1800 Final Exam
SHOW ALL WORK IN A BLUE BOOK:
Only MINIMAL CREDIT will be awarded for answers without supporting work.
1. (10 pts.)
Solve :
3
x
°
1
+
x
x
+ 1
<
1
2. (8 pts.)
Find the domain of the function given by
f
(
x
) =
e
x
2
°
1
+ ln (4
x
°
x
3
) + cos
x
3. (10 pts.)
Let
f
(
x
) =
x
2
°
4
x
+ 5
and
g
(
x
) = 6
°
x
2
:
Find and simplify completely
(a)
(
g
±
f
) (
x
)
(b)
f
(
x
+
h
)
°
f
(
x
)
h
4. (6 pts.)
Let
f
(
x
) =
8
x
°
4
2
x
+ 6
:
Find
f
°
1
(
x
)
;
where
f
°
1
is the inverse function of
f:
5. (10 pts.) A painter has 200 feet of very thin tape (shown here as solid black lines).
He is
going to use it to enclose a large rectangle on a basketball court.
He is also going to use a
piece of tape to partition the rectangle in half (see °gure).
Express the area
A
of the large
rectangle as a function of
x
.
6. (10 pts.)
A manufacturer of radios has daily production costs of
C
= 800
°
10
x
+ 0
:
25
x
2
where
C
is the total cost (in dollars) and
x
is the number of radios produced.
How many
radios should be produced each day to yield a minimum cost?
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 Spring '09
 Calculus, pts, Inverse function, Polar coordinate system, blue book

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