bz In Exercises 15-28, use Theorem 1 to determine the limit of the sequence or state that the sequence diverges. 15) an = 5-2n 5n 4 n2 4+n-3n² 16. an 20- -
bz In Exercises 15-28, use Theorem 1 to determine the limit of the sequence or state that the sequence diverges. 15) an = 5-2n 5n 4 n2 4+n-3n² 16. an 20- -
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Can you help me solve 15? Theorem 1 says that a_n= f(n).
![ero?
• Bounded monotonic sequences converge (Theorem 6).
(¹)"
F. That is, a₁ = 1,
(c)
vely?
timi
her og
terms of
rting
(b) b = √√√4+bn-1
5.
Theorem 5 says that every convergent sequence is bounded. Deter-
mine if the following statements are true or false, and if false, give a coun-
terexample:
(a) If (an) is bounded, then it converges.
(b) If [an] is not bounded, then it diverges.
(c) If (an) diverges, then it is not bounded.
(a) an = √4+n
14. Suppose that lim an = 4 and lim bn = 7. Determine:
848
818
(a) lim (an + bn)
848
(c) lim cos(лbn)
818
17, bn =
In Exercises 15-28, use Theorem 1 to determine the limit of the sequence
or state that the sequence diverges.
13
oryang art nl
15) an = 5 - 2n
12581/1)-n
drive (19. an = 252
21. Cn = 9n
23. an =
25. an In
27. Zn =
5n -1
12n +9
29, an=
√n² +1
n
4+
12n+2
-9+4n
n
(b) lim a
1148
screa
mil straw 3
(d) lim (a-2anbn)
818
TH
18. an =
16. an 20-
20. Zn =
n+1
en
28. yn = ne¹/n
900Sunga
In Exercises 29-32, use Theorem 4 to determine the limit of the sequenc
=e4n/(3n+9)
4
-n²
4+n-3n²
4n² +1
n
(3)
10-1/n
22. Zn =
24. an =
n
√n³+1
26. rn = Inn - In(n² + 1)
30. an](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3f7c47f-f942-4013-9970-37881347efaf%2Fa48eb886-b3f4-4d5d-8204-ac5b7b3e269a%2Fiwkjbog_processed.jpeg&w=3840&q=75)
Transcribed Image Text:ero?
• Bounded monotonic sequences converge (Theorem 6).
(¹)"
F. That is, a₁ = 1,
(c)
vely?
timi
her og
terms of
rting
(b) b = √√√4+bn-1
5.
Theorem 5 says that every convergent sequence is bounded. Deter-
mine if the following statements are true or false, and if false, give a coun-
terexample:
(a) If (an) is bounded, then it converges.
(b) If [an] is not bounded, then it diverges.
(c) If (an) diverges, then it is not bounded.
(a) an = √4+n
14. Suppose that lim an = 4 and lim bn = 7. Determine:
848
818
(a) lim (an + bn)
848
(c) lim cos(лbn)
818
17, bn =
In Exercises 15-28, use Theorem 1 to determine the limit of the sequence
or state that the sequence diverges.
13
oryang art nl
15) an = 5 - 2n
12581/1)-n
drive (19. an = 252
21. Cn = 9n
23. an =
25. an In
27. Zn =
5n -1
12n +9
29, an=
√n² +1
n
4+
12n+2
-9+4n
n
(b) lim a
1148
screa
mil straw 3
(d) lim (a-2anbn)
818
TH
18. an =
16. an 20-
20. Zn =
n+1
en
28. yn = ne¹/n
900Sunga
In Exercises 29-32, use Theorem 4 to determine the limit of the sequenc
=e4n/(3n+9)
4
-n²
4+n-3n²
4n² +1
n
(3)
10-1/n
22. Zn =
24. an =
n
√n³+1
26. rn = Inn - In(n² + 1)
30. an
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