MATH 1100-001
EXAM I
Instructions:. Put your name on the exam. Show your work for full credit. Calculators and other electronic
devices (including cell phones) are not allowed. You are allowed one side of an 8.5 by 11 inch sheet of notes.
1. (5 points each) For
f(x)
= x2x_2
evaluate the following limits:
a.
-l
lirn
—1
f(x)
-_
(‘
1
0
—1
I
—
a
b. limf(x)
x—* 1
-
0
/ —I
.
-r
c. lim
‘4
f(x)
J N
c/h
FI
kv
X
_,
C,—’
d. At what points is f(x) discontinuous?
1io
4
y
ev
-
=
—
I.
‘
Ii
(J
c-\)
I
N
fJ
r\J
+
>
‘—.
.3—
+
r’J
N
I
J)c
j)c
j1
3J
I>c
N
I)
II
_1_)
U
-
CD
SD
CD
C
CD
I.
.cs
C
C)
I
Cj
—
c:)
¼
II
‘
c
c)
II
.z:
c
.-
+
D/3N
0
0
)I
f\J
Il
1”
4-
cl
rJ
+
CD
C
>(
(A)—
+
+
‘1
,,
+1
><L?
jr)
+
>c
Ii
-I
+
r
-4-)
crJ
+
‘N
N
Jo’J
1
•
U)
I
>‘-
(%)Lfl
1
J
xI
u
o-,
<Cj1
‘j
+
U
U)
C
c-fl
5. (5 points each) Suppose that the revenue for selling x calculators is R(x) = lOOx + 0.05x
.
2
a. Find the rate of change of the revenue with respect to the number of calculators sold.
b. What is the rate of change of the revenue when 100 calculators are sold?
P
/)+
,
/ /617
-
()
6. (5 points each) Evaluate the following:
a. lirii
x—*oo
2—3x
3
3 x
2x
—
/
1u1/5
a.
lim
x—--Do
+
x
—
3
1
X + 1
w’
>L
/