Calculus Early Transcendentals– 11th
ST
Edition
UV
SOLUTIONS
IA
MANUAL
_A
PP
Howard Anton, Irl C. Bivens & Stephen Davis
RO
Complete Solutions Manual for Instructors and
VE
Students
D?
© Howard Anton, Irl C. Bivens & Stephen Davis
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©MEDGEEK
, rch 26,
arch 26, 2009
2009 06:39
06:39 ”ISM
”ISM LT
LT chapter
chapter 1”
1” Sheet
Sheet number
number 11 Page
Page number
number 26
26 black
black
CHAPTER
CHAPTER 11
Limits
Limits and
and Continuity
Limits and Continuity Continuity
ST
EXERCISE
EXERCISE SET
SET 1.1
1.1
Exercise
1. (a) 33 Set 1.1
1. (a) (b)
(b) 33 (c)
(c) 33 (d)
(d) 33
UV
1. (a) 30
2. (b) 3 (c) 3 (d) 3
2. (a)
(a) 0 (b)
(b) 00 (c)
(c) 00 (d)
(d) 00
2. (a) 0 (b) 0 (c) 0 (d) 0
3. (a) −1
3. (a) −1 (b)
(b) 33 (c)
(c) does
does not
not exist
exist (d)
(d) 11
3. (a) −1 (b) 3 (c) does not exist (d) 1
4.
4. (a)
(a) 22 (b)
(b) 00 (c)
(c) does
does not
not exist
exist (d)
(d) 22
IA
4. (a) 2 (b) 0 (c) does not exist (d) 2
5.
5. (a)
(a) 00 (b)
(b) 00 (c)
(c) 00 (d)
(d) 33
5. (a) 0 (b) 0 (c) 0 (d) 3
6.
6. (a)
(a) 11 (b) 1
(b) 1 (c) 1
(c) 1 (d)
(d) 00
6. (a) 1 (b) 1 (c) 1 (d) 0
_A
7.
7. (a)
(a) −∞
−∞ (b) −∞
(b) −∞ (c) −∞
(c) −∞ (d)
(d) 11
7. (a) −∞ (b) −∞ (c) −∞ (d) 1
8.
8. (a) +∞
(a) +∞
+∞ (b) +∞
(b) +∞
+∞ (c) +∞
(c) +∞
+∞ (d) undef
(d) can
undef
8. (a) (b) (c) (d) not be found from graph
9. (a) 11 (b) −∞ (c) does not
not exist
exist (f ) (d) −2
PP
9. (a) +∞
9. (a) −∞ 2
(b) +∞ (b) (c) (d) 2 (c) (e)
does−∞ x(d) −2x = 0, x = 2
= −2,
10. (a)
10. (a) +∞
(a) does
+∞not exist (b)
(b) 11
(b)−∞ (c) 0 (c)
(c)−1does
(d) does not
(e)exist
not +∞
exist (d)
(f
(d)) 322 (g) x = −2, x = 2
11.
11. (i)
11. (i)
(i) −0.1
−0.1 −0.01
−0.01 −0.001
−0.001 0.001
0.001 0.01
0.01 0.1
0.1
−0.1 −0.01 −0.001 0.001 0.01 0.1
RO
1.9866933
1.9866933 1.9998667
1.9998667 1.9999987
1.9999987 1.9999987
1.9999987 1.9998667
1.9998667 1.9866933
1.9866933
1.9866933 1.9998667 1.9999987 1.9999987 1.9998667 1.9866933
(ii)
(ii)
2.
2. The
The limit
limit appears
appears to
to be
be 2.
2.
VE
1.986
-0.1 0.1
1.986
-0.1 0.1
(ii) The limit appears to be 2.
12. (i)
12.
12. (i)
(i) −0.5 −0.05 −0.005 0.005 0.05 0.5
−0.5 −0.05 −0.005 0.005 0.05 0.5
−0.489669752 −0.499895842 −0.499998958 −0.499998958 −0.499895842 −0.489669752
D?
−0.489669752 −0.499895842 −0.499998958 −0.499998958 −0.499895842 −0.489669752
(ii)
(ii) -0.4896698
-0.4896698 The
The limit
limit appears
appears to be −1/2.
to be −1/2.
??
-0.5
-0.5
-0.5 0.5
(ii) -0.5 0.5 The limit appears to be −1/2.
13. 1
13. (a)
(a) 22 1.5
1.5 1.1
1.1 1.01
1.01 1.001
1.001 00 0.5
0.5 0.9
0.9 0.99
0.99 0.999
0.999
0.1429 0.2105 0.3021 0.3300 0.3330 1.0000 0.5714 0.3690 0.3367 0.3337
0.1429 0.2105 0.3021 0.3300 0.3330 1.0000 0.5714 0.3690 0.3367 0.3337
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, 2 Chapter 1
13. (a) 2 1.5 1.1 1.01 1.001 0 0.5 0.9 0.99 0.999
0.1429 0.2105 0.3021 0.3300 0.3330 1.0000 0.5714 0.3690 0.3367 0.3337
1
ST
0 2
0 The limit is 1/3.
UV
(b) 2 1.5 1.1 1.01 1.001 1.0001
0.4286 1.0526 6.344 66.33 666.3 6666.3
50
IA
1 2
0 The limit is +∞.
_A
(c) 0 0.5 0.9 0.99 0.999 0.9999
−1 −1.7143 −7.0111 −67.001 −667.0 −6667.0
PP
0
0 1
RO
-50 The limit is −∞.
14. (a) −0.25 −0.1 −0.001 −0.0001 0.0001 0.001 0.1 0.25
0.5359 0.5132 0.5001 0.5000 0.5000 0.4999 0.4881 0.4721
VE
0.6
D?
-0.25 0.25
0 The limit is 1/2.
(b) 0.25 0.1 0.001 0.0001
??
8.4721 20.488 2000.5 20001
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, Exercise Set 1.1 3
100
0 0.25
0 The limit is +∞.
ST
(c) −0.25 −0.1 −0.001 −0.0001
−7.4641 −19.487 −1999.5 −20000
0
-0.25 0
UV
-100 The limit is −∞.
IA
15. (a) −0.25 −0.1 −0.001 −0.0001 0.0001 0.001 0.1 0.25
2.7266 2.9552 3.0000 3.0000 3.0000 3.0000 2.9552 2.7266
3
_A
PP
-0.25 0.25
2 The limit is 3.
(b) 0 −0.5 −0.9 −0.99 −0.999 −1.5 −1.1 −1.01 −1.001
1 1.7552 6.2161 54.87 541.1 −0.1415 −4.536 −53.19 −539.5
RO
60
-1.5 0
VE
-60 The limit does not exist.
16. (a) 0 −0.5 −0.9 −0.99 −0.999 −1.5 −1.1 −1.01 −1.001
1.5574 1.0926 1.0033 1.0000 1.0000 1.0926 1.0033 1.0000 1.0000
D?
1.5
??
-1.5 0
1 The limit is 1.
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ST
Edition
UV
SOLUTIONS
IA
MANUAL
_A
PP
Howard Anton, Irl C. Bivens & Stephen Davis
RO
Complete Solutions Manual for Instructors and
VE
Students
D?
© Howard Anton, Irl C. Bivens & Stephen Davis
All rights reserved. Reproduction or distribution without permission is prohibited.
??
©MEDGEEK
, rch 26,
arch 26, 2009
2009 06:39
06:39 ”ISM
”ISM LT
LT chapter
chapter 1”
1” Sheet
Sheet number
number 11 Page
Page number
number 26
26 black
black
CHAPTER
CHAPTER 11
Limits
Limits and
and Continuity
Limits and Continuity Continuity
ST
EXERCISE
EXERCISE SET
SET 1.1
1.1
Exercise
1. (a) 33 Set 1.1
1. (a) (b)
(b) 33 (c)
(c) 33 (d)
(d) 33
UV
1. (a) 30
2. (b) 3 (c) 3 (d) 3
2. (a)
(a) 0 (b)
(b) 00 (c)
(c) 00 (d)
(d) 00
2. (a) 0 (b) 0 (c) 0 (d) 0
3. (a) −1
3. (a) −1 (b)
(b) 33 (c)
(c) does
does not
not exist
exist (d)
(d) 11
3. (a) −1 (b) 3 (c) does not exist (d) 1
4.
4. (a)
(a) 22 (b)
(b) 00 (c)
(c) does
does not
not exist
exist (d)
(d) 22
IA
4. (a) 2 (b) 0 (c) does not exist (d) 2
5.
5. (a)
(a) 00 (b)
(b) 00 (c)
(c) 00 (d)
(d) 33
5. (a) 0 (b) 0 (c) 0 (d) 3
6.
6. (a)
(a) 11 (b) 1
(b) 1 (c) 1
(c) 1 (d)
(d) 00
6. (a) 1 (b) 1 (c) 1 (d) 0
_A
7.
7. (a)
(a) −∞
−∞ (b) −∞
(b) −∞ (c) −∞
(c) −∞ (d)
(d) 11
7. (a) −∞ (b) −∞ (c) −∞ (d) 1
8.
8. (a) +∞
(a) +∞
+∞ (b) +∞
(b) +∞
+∞ (c) +∞
(c) +∞
+∞ (d) undef
(d) can
undef
8. (a) (b) (c) (d) not be found from graph
9. (a) 11 (b) −∞ (c) does not
not exist
exist (f ) (d) −2
PP
9. (a) +∞
9. (a) −∞ 2
(b) +∞ (b) (c) (d) 2 (c) (e)
does−∞ x(d) −2x = 0, x = 2
= −2,
10. (a)
10. (a) +∞
(a) does
+∞not exist (b)
(b) 11
(b)−∞ (c) 0 (c)
(c)−1does
(d) does not
(e)exist
not +∞
exist (d)
(f
(d)) 322 (g) x = −2, x = 2
11.
11. (i)
11. (i)
(i) −0.1
−0.1 −0.01
−0.01 −0.001
−0.001 0.001
0.001 0.01
0.01 0.1
0.1
−0.1 −0.01 −0.001 0.001 0.01 0.1
RO
1.9866933
1.9866933 1.9998667
1.9998667 1.9999987
1.9999987 1.9999987
1.9999987 1.9998667
1.9998667 1.9866933
1.9866933
1.9866933 1.9998667 1.9999987 1.9999987 1.9998667 1.9866933
(ii)
(ii)
2.
2. The
The limit
limit appears
appears to
to be
be 2.
2.
VE
1.986
-0.1 0.1
1.986
-0.1 0.1
(ii) The limit appears to be 2.
12. (i)
12.
12. (i)
(i) −0.5 −0.05 −0.005 0.005 0.05 0.5
−0.5 −0.05 −0.005 0.005 0.05 0.5
−0.489669752 −0.499895842 −0.499998958 −0.499998958 −0.499895842 −0.489669752
D?
−0.489669752 −0.499895842 −0.499998958 −0.499998958 −0.499895842 −0.489669752
(ii)
(ii) -0.4896698
-0.4896698 The
The limit
limit appears
appears to be −1/2.
to be −1/2.
??
-0.5
-0.5
-0.5 0.5
(ii) -0.5 0.5 The limit appears to be −1/2.
13. 1
13. (a)
(a) 22 1.5
1.5 1.1
1.1 1.01
1.01 1.001
1.001 00 0.5
0.5 0.9
0.9 0.99
0.99 0.999
0.999
0.1429 0.2105 0.3021 0.3300 0.3330 1.0000 0.5714 0.3690 0.3367 0.3337
0.1429 0.2105 0.3021 0.3300 0.3330 1.0000 0.5714 0.3690 0.3367 0.3337
Downloaded by: tutorsection | Want to earn $1.236
Distribution26
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, 2 Chapter 1
13. (a) 2 1.5 1.1 1.01 1.001 0 0.5 0.9 0.99 0.999
0.1429 0.2105 0.3021 0.3300 0.3330 1.0000 0.5714 0.3690 0.3367 0.3337
1
ST
0 2
0 The limit is 1/3.
UV
(b) 2 1.5 1.1 1.01 1.001 1.0001
0.4286 1.0526 6.344 66.33 666.3 6666.3
50
IA
1 2
0 The limit is +∞.
_A
(c) 0 0.5 0.9 0.99 0.999 0.9999
−1 −1.7143 −7.0111 −67.001 −667.0 −6667.0
PP
0
0 1
RO
-50 The limit is −∞.
14. (a) −0.25 −0.1 −0.001 −0.0001 0.0001 0.001 0.1 0.25
0.5359 0.5132 0.5001 0.5000 0.5000 0.4999 0.4881 0.4721
VE
0.6
D?
-0.25 0.25
0 The limit is 1/2.
(b) 0.25 0.1 0.001 0.0001
??
8.4721 20.488 2000.5 20001
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, Exercise Set 1.1 3
100
0 0.25
0 The limit is +∞.
ST
(c) −0.25 −0.1 −0.001 −0.0001
−7.4641 −19.487 −1999.5 −20000
0
-0.25 0
UV
-100 The limit is −∞.
IA
15. (a) −0.25 −0.1 −0.001 −0.0001 0.0001 0.001 0.1 0.25
2.7266 2.9552 3.0000 3.0000 3.0000 3.0000 2.9552 2.7266
3
_A
PP
-0.25 0.25
2 The limit is 3.
(b) 0 −0.5 −0.9 −0.99 −0.999 −1.5 −1.1 −1.01 −1.001
1 1.7552 6.2161 54.87 541.1 −0.1415 −4.536 −53.19 −539.5
RO
60
-1.5 0
VE
-60 The limit does not exist.
16. (a) 0 −0.5 −0.9 −0.99 −0.999 −1.5 −1.1 −1.01 −1.001
1.5574 1.0926 1.0033 1.0000 1.0000 1.0926 1.0033 1.0000 1.0000
D?
1.5
??
-1.5 0
1 The limit is 1.
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