/v
1. (5 pts each) For
,answer the following questions.
li,nf(x)
(a)
fe&
=
-
(i
34)( xi
—
-
4’I fr1
—3
)c3
)(34
X3
I
_
Y3
$
(fri
(-I?*)
limf(x)
=
—
—
q-o
—
q
1(x) discontinuous?
=3)
IA
j
‘
(d) Whereis
b
.
(3
3
(c)
)
7iV
=
(b)
”
4
Ii L
(
Oiy a
fri.
1
W
/
2. (5 pts each) Find the following limits.
+5x—3
2
.x
=
Jim
(a)
2x’+7x
-,
1
_L
/
/
L)
5L
---
1-S?c—
lx
Iz,
-i
)(Z..
-.--
Jim
(b)
0
+x—2
3
x
=
+4x+1
5
3x
U
2).
-z
-
-.
Lf/
k’)
3. (12 pts) Use the definition of the derivative to find
+3x
2
f(x)=x
4
f ‘(x)
for
,;
j1
0—
0
:3
A____
11
1
t3
ft
li-)J
f’(x)
2A
=
4. (6 pts each) Suppose the total cost of producing x bicycles is given by
2
C(x)=5000+40x+O.5x
(a) How fast is the Cost changing with respect to the number of bicycles
produced?
X
Answer:
(b) What is the rate of change of the Cost function when 10 bicycles are
produced?
/D
=Y
Answer:
y’ for the following functions.
5. (5 pts each) Find
(a)
(,
y=/x—+4x—7x’
3’-
..L.
5
2x
-
(-2
)5
7
(b)
—
(Do NOT bother to simplify!!!)
2
(/) 7)(
s*
cx
x
(
1
)
3
y=(4x4+x2)(sx+,
(Yx
—
=
3A
(J
)(cx
)
(9+
XT)
<
CD
a
0
0
CD
<
CD
0
0
In
-4
I
II
-
-,-
)c
LI
4
LF)
N1
cj-7
/—-
+
Cv1
+
‘2
ii
II
2
>c
ri
‘1
>c
>
Lj
1
r.
(-“S
‘I
—
CD
0
0
—I
z
0
0
D
In
0
DCD
(a
0
00
Lu
0
D
CD
Co
(A)
>
3
\J-J
(S
—
/
cç
<
I
-‘
—S’
—
4-
L
cJ
•
-.
>(
><
>c
)
(‘J
x
CD
D
D
CD
a
5-
CD
CD
-Q
0.
><
II
<
CD