Download For the function f graphed in the accompanying figure, find 1) (a) 1 (b

King Fahd University of Petroleum and Minerals
College of Sciences
MATH 101 Calculus I
Department of Mathematical Sciences
Instructor: Dr. Faisal Fairag
EXAM (1) FORM B
For the function f graphed in the
accompanying figure, find
1) lim f ( x ) = (see figure)
x →1
(Ex 1, pg 165)
2) lim f ( x ) = (see figure)
3) lim f ( x ) = (see figure)
(a) 1
(b) -1
(c) 3
(d) -3
(e) does not exist
4) lim f ( x ) = (see figure)
(Ex 1, pg 165)
(Ex 1, pg 165)
(Ex 1, pg 165)
(a) 1
(b) -1
(c) 3
(d) -3
(e) does not exist
5) lim f ( x ) = (see figure)
(a) 1
(b) -1
(c) 2
(d) -2
(e) does not exist
6) lim f ( x ) = (see figure)
1
-1
4
-4
does not exist
7) lim+ f ( x ) = (see figure)
(Ex 1, pg 165)
(Ex 1, pg 165)
(Ex 1, pg 165)
(a) 1
(b) -1
(c) 3
(d) 0
(e) does not exist
8) lim f ( x ) = (see figure)
(a) 1
(b) -1
(c) 3
(d) -3
(e) does not exist
9) lim− f ( x ) = (see figure)
(Ex 1, pg 165)
(Ex 1, pg 165)
x →3
x →−∞
x →0
(a) 1
(b) -1
(c) 2
1
(d)
2
(e) does not exist
x −9
10) Find lim
= (Ex29, pg130)
x →9
x −3
(f) 3
(g) -3
(h) 6
(i) -6
(j) does not exist
x →2
x →+∞
x →4
x →3
(a)
(b)
(c)
(d)
(e)
1
-1
3
0
does not exist
x →3
(a)
(b)
(c)
(d)
(e)
1
-1
2
-2
does not exist
11) Find lim−
x →2
(a)
(b)
(c)
(d)
(e)
0
2
-2
+∞
−∞
x
= (Ex19, pg130)
x −4
2
12) Find lim−
x →4
(Ex25, pg130)
(a)
(b)
(c)
(d)
(e)
4
8
-8
+∞
−∞
3−x
=
x − 2x − 8
2
x−2
=
x →−∞ x + 2 x + 1
13) Find lim
2
(Ex15, pg136)
(a)
(b)
(c)
(d)
(e)
0
-2
2
+∞
−∞
16) Find lim
x →−∞
(Ex23, pg137)
x2 + 6x + 5
=
x →−1 x 2 − 3x − 4
14) Find lim
15) Find lim
(Ex11, pg130)
(Ex17, pg136)
−
3
(a)
8
(b) 3
(c) 8
(d) + ∞
(e) − ∞
19) Find the values of x (if any)
at which f is not continuous.
x−4
f (x ) = 2
(Ex17, pg157)
x − 16
(a) x= 0, 4
(b) x= 0, -4
(c) x= 0, 4, -4
(d) x= 4, -4
(e) x= 0
4
5
2− y
7 + 6y2
=
1
+∞
−∞
20) Given lim (7x + 5) = − 2, ε = 0.01
x →− 1
find a number δ such that
f ( x) − L < ε if 0 < x − a < δ
(Ex11, pg145)
(a) δ =
(e) δ
x−2
, which statement is true (Ex29(a), pg157)
x −2
f has removable discontinuity at x = ±2
f has removable discontinuity at x=2 and a not removable
discontinuity at x=-2
f has removable discontinuity at x=2 and a continuity at x=-2
lim f ( x ) = 0
22) Let f ( x ) =
x →+2
(e) lim f ( x ) = 1
x →−2
18) Find lim ( x 2 + 3 − x ) =
x →+∞
(Ex31, pg137)
0
3
-3
1
7
1
6
(b) δ
5
2
-5
+∞
−∞
(Ex21, pg137)
1
400
1
=
500
1
=
550
1
=
600
1
=
700
2 + 3x − 5 x 2
=
1 + 8x 2
5
2
−3
y → −∞
(d) δ
(c)
(d)
−
17) Find lim
(c) δ
(a)
(b)
x →+∞
5
4
0
+∞
−∞
3x4 + x
=
x2 −8
3
(a) + ∞
(b) − ∞
21) Find the values of x (if any)
at which f is not continuous.
x
f (x ) =
(Ex19, pg157)
x −3
(a) x= 0, 3
(b) x= 0, -3
(c) x= 0, 3, -3
(d) x= 3, -3
(e) x= 0
23) Let f ( x ) =
x
x
, which
statement is true (Ex29(c), pg157)
(a) f has a removable
discontinuity at x=0
(b) f(0)= 1
(c) lim f ( x ) = 1
x →0
(d) f is continuous at x=0
(e) f is discontinuous at x=0
King Fahd University of Petroleum and Minerals
College of Sciences
MATH 101 Calculus I
EXAM (1) FORM B
ID #
Name:
k 2 x + 1

24) f ( x ) = k + 1
3kx − 1

Department of Mathematical Sciences
Instructor: Dr. Faisal Fairag
x>1
x =1
x <1
(a) Find the values of k so that the function f has a removable discontinuity at x=1
(SHOW ALL YOUR WORK)
(b) Find the values of k so that the function f is continuous from the left at x=1
(SHOW ALL YOUR WORK)
Sec # (11) (28)
25) State the intermediate value theorem.
Multiple Choice Answers
(Fill the Correct Circle)
FORM B
1
2
3
4
x 4 + x 2 + 3x
(SHOW ALL YOUR WORK)
x →−∞
x +1
26) Find lim
5
6
7
8
9
10
11
12
13
14
15
16
17
18
27) Find lim
h→ 0
2+h −2
h
19
(SHOW ALL YOUR WORK)
20
21
22
23
a
b
c
d
e
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Question
MCQ
24 (a)
24 (b)
25
26
27
Mark