Calculus: Early Transcendentals
11th Edition
ST
SOLUTIONS
UV
MANUAL
IA
_A
Howard Anton
PP
Irl Bivens
Stephen Davis
RO
VE
Comprehensive Solutions Manual for
D?
Instructors and Students
© Howard Anton, Irl Bivens & Stephen Davis. All rights reserved. Reproduction or
distribution without permission is prohibited.
©MedConnoisseur
, Solutions Manual for
Calculus Early
ST
Transcendentals 11e
UV
Howard Anton, Irl
Bivens, Stephen Davis
IA
(All Chapters)
_A
PP
RO
VE
D?
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, 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
EXERCISE
EXERCISE SET
SET 1.1
1.1
ST
Exercise
1. (a) 33 Set 1.1
1. (a) (b)
(b) 33 (c)
(c) 33 (d)
(d) 33
1. (a) 30
2. (b) 3 (c) 3 (d) 3
2. (a)
(a) 0 (b)
(b) 00 (c)
(c) 00 (d)
(d) 00
UV
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
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
IA
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
7.
7. (a)
(a) −∞
−∞ (b) −∞
(b) −∞ (c) −∞
(c) −∞ (d)
(d) 11
7. (a) −∞ (b) −∞ (c) −∞ (d) 1
_A
8.
8. (a) +∞
(a) +∞
+∞ (b) +∞
(b) +∞
+∞ (c) +∞
(c) +∞
+∞ (d) undef
(d) can
undef
8. (a) (b) (c) (d) not be found from graph
9.
9. (a) 11
(a) +∞ (b) −∞
−∞ 2 (c) does not
not exist
exist (f ) (d) −2
−2x = 0, x = 2
9. (a) (b) +∞ (b) (c) (d) 2 (c) (e)
does−∞ x(d)
= −2,
10. (a) +∞ (b) 11 (c)
(c)−1does
does not
(e)exist (d)) 322
PP
10. (a)
(a) does
+∞not exist (b)−∞
(b) (c) 0 (d) not +∞
exist (f
(d) (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
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.
RO
The
The limit
limit appears
appears to
to be
be 2.
2.
1.986
-0.1 0.1
1.986
-0.1 0.1
(ii) The limit appears to be 2.
VE
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
−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
D?
−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
0 2
ST
0 The limit is 1/3.
(b) 2 1.5 1.1 1.01 1.001 1.0001
0.4286 1.0526 6.344 66.33 666.3 6666.3
UV
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
0
0 1
PP
-50 The limit is −∞.
RO
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
0.6
VE
-0.25 0.25
D?
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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11th Edition
ST
SOLUTIONS
UV
MANUAL
IA
_A
Howard Anton
PP
Irl Bivens
Stephen Davis
RO
VE
Comprehensive Solutions Manual for
D?
Instructors and Students
© Howard Anton, Irl Bivens & Stephen Davis. All rights reserved. Reproduction or
distribution without permission is prohibited.
©MedConnoisseur
, Solutions Manual for
Calculus Early
ST
Transcendentals 11e
UV
Howard Anton, Irl
Bivens, Stephen Davis
IA
(All Chapters)
_A
PP
RO
VE
D?
Downloaded by: tutorsection | Want to earn $1.236
Distribution of this document is illegal extra per year?
, 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
EXERCISE
EXERCISE SET
SET 1.1
1.1
ST
Exercise
1. (a) 33 Set 1.1
1. (a) (b)
(b) 33 (c)
(c) 33 (d)
(d) 33
1. (a) 30
2. (b) 3 (c) 3 (d) 3
2. (a)
(a) 0 (b)
(b) 00 (c)
(c) 00 (d)
(d) 00
UV
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
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
IA
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
7.
7. (a)
(a) −∞
−∞ (b) −∞
(b) −∞ (c) −∞
(c) −∞ (d)
(d) 11
7. (a) −∞ (b) −∞ (c) −∞ (d) 1
_A
8.
8. (a) +∞
(a) +∞
+∞ (b) +∞
(b) +∞
+∞ (c) +∞
(c) +∞
+∞ (d) undef
(d) can
undef
8. (a) (b) (c) (d) not be found from graph
9.
9. (a) 11
(a) +∞ (b) −∞
−∞ 2 (c) does not
not exist
exist (f ) (d) −2
−2x = 0, x = 2
9. (a) (b) +∞ (b) (c) (d) 2 (c) (e)
does−∞ x(d)
= −2,
10. (a) +∞ (b) 11 (c)
(c)−1does
does not
(e)exist (d)) 322
PP
10. (a)
(a) does
+∞not exist (b)−∞
(b) (c) 0 (d) not +∞
exist (f
(d) (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
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.
RO
The
The limit
limit appears
appears to
to be
be 2.
2.
1.986
-0.1 0.1
1.986
-0.1 0.1
(ii) The limit appears to be 2.
VE
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
−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
D?
−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
0 2
ST
0 The limit is 1/3.
(b) 2 1.5 1.1 1.01 1.001 1.0001
0.4286 1.0526 6.344 66.33 666.3 6666.3
UV
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
0
0 1
PP
-50 The limit is −∞.
RO
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
0.6
VE
-0.25 0.25
D?
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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