King Fahd University of Petroleum & Minerals
Department of Mathematics and Statistics
MATH 101 – Calculus I
EXAM I
20092010 (091)
Monday, November 2, 2009
Allowed Time: 2 Hours
Name:
ID Number:
Serial Number:
Section Number:
Instructor’s Name:
Instrunctions
:
1. Write neatly and legibly. You may lose points for messy work.
2.
Show all your work.
No points for answers without justification.
3.
Calculators and Mobiles are not allowed
.
4. Make sure that you have 10 different problems (6 pages + cover page).
Problem No.
Points
Maxiumum Points
1
12
2
7
3(a,b,c)
18
4
12
5
6
6
10
7
7
8
12
9
12
10
4
Total:
100
MATH 101 EXAM I (Term 091)
Page
1 of 6
1. (12points) Sketch the graph of a function
f
that satisfies all of the following conditions:
lim
x
→−
4

f
(
x
) =
−∞
;
lim
x
→−
4
+
f
(
x
) =
∞
;
lim
x
→−∞
f
(
x
) = 0;
lim
x
→−
2
f
(
x
) = 1 ;
f
is undefined at
−
2;
lim
x
→
1

f
(
x
) =
−
1 ;
lim
x
→
1
+
f
(
x
) = 2 ;
f
(1) = 1
O
N
±
!
"
¡
"
¡
¡
±
¡
!
2. (7points) If
x
3
−
x
+ 4
≤
x
+
f
(
x
)
≤
3
x
2
+ 1 for all real numbers
x
, then find lim
x
→
1
f
(
x
).
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 Math, Calculus, Statistics