Solutions Manual for
Calculus Early
Transcendentals 11e
Howard Anton, Irl
Bivens, Stephen Davis
(All Chapters)
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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
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
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
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
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)
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
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.
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
−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
0 2
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
50
1 2
0 The limit is +∞.
(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
-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
0.6
-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 +∞.
(c) −0.25 −0.1 −0.001 −0.0001
−7.4641 −19.487 −1999.5 −20000
0
-0.25 0
-100 The limit is −∞.
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
-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
60
-1.5 0
-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
1.5
-1.5 0
1 The limit is 1.
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Calculus Early
Transcendentals 11e
Howard Anton, Irl
Bivens, Stephen Davis
(All Chapters)
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
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
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
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
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)
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
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.
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
−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
0 2
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
50
1 2
0 The limit is +∞.
(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
-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
0.6
-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 +∞.
(c) −0.25 −0.1 −0.001 −0.0001
−7.4641 −19.487 −1999.5 −20000
0
-0.25 0
-100 The limit is −∞.
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
-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
60
-1.5 0
-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
1.5
-1.5 0
1 The limit is 1.
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