Subtiers or Series Limit Type Tier Expression Notes Examples Convergence Two examples Super Large an = n" N/A among many An = n! т" 3n Exponentially Large Am = q", lq| > 1 Larger |q|, larger tier en (-2)" (3/2)" ne lim an = ∞ n2 n=1 An = n°, s > 0 Larger s, larger tier Positive Power Diverges Vn n?/3 [In(n)]? Positive An = [In(n)]ª, Larger s, larger tier Logarithmic In(n) Power [In(n)]1/2 and 1/an 2n e.g. an = C + 0, an = (-1)", an = Both An Bounded are bounded n +1 Negative Logarithmic an = [In(n)]®, s < 0 Larger s, larger tier [In(n)]¬1/2 1/ In(n) ±an n=1 [In(n)]-2 1//n Power Diverges Or Converges Conditionally* Negative Power Larger s, larger tier An = n°, Twilight Realm* 1.0000001 -2 п lim an = 0 (1/2)" e-n Exponentially Small Larger |q|, larger tier an = q", An 0 < [q| < 1 1/(-3)" n=1 Converges Absolutely Super Small Two examples an = e" /n! N/A among many ат, — п Zero Smallest With the help of the "tierlist", sort the following sequences in descending order: dn (-1)" + 3/In(n) bn n' +n-" An Сп en fn In п e" — (-4)" | т" sin(-n) + (-1)" п-е е—п u-
Subtiers or Series Limit Type Tier Expression Notes Examples Convergence Two examples Super Large an = n" N/A among many An = n! т" 3n Exponentially Large Am = q", lq| > 1 Larger |q|, larger tier en (-2)" (3/2)" ne lim an = ∞ n2 n=1 An = n°, s > 0 Larger s, larger tier Positive Power Diverges Vn n?/3 [In(n)]? Positive An = [In(n)]ª, Larger s, larger tier Logarithmic In(n) Power [In(n)]1/2 and 1/an 2n e.g. an = C + 0, an = (-1)", an = Both An Bounded are bounded n +1 Negative Logarithmic an = [In(n)]®, s < 0 Larger s, larger tier [In(n)]¬1/2 1/ In(n) ±an n=1 [In(n)]-2 1//n Power Diverges Or Converges Conditionally* Negative Power Larger s, larger tier An = n°, Twilight Realm* 1.0000001 -2 п lim an = 0 (1/2)" e-n Exponentially Small Larger |q|, larger tier an = q", An 0 < [q| < 1 1/(-3)" n=1 Converges Absolutely Super Small Two examples an = e" /n! N/A among many ат, — п Zero Smallest With the help of the "tierlist", sort the following sequences in descending order: dn (-1)" + 3/In(n) bn n' +n-" An Сп en fn In п e" — (-4)" | т" sin(-n) + (-1)" п-е е—п u-
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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Question
descending order = largest comes first
![Subtiers or
Series
Limit Type
Tier
Expression
Notes
Examples
Convergence
Two examples
Super
Large
an = n"
N/A
among many
An = n!
т"
3n
Exponentially
Large
Am = q",
lq| > 1
Larger |q|,
larger tier
en
(-2)"
(3/2)"
ne
lim an = ∞
n2
n=1
An = n°,
s > 0
Larger s,
larger tier
Positive
Power
Diverges
Vn
n?/3
[In(n)]?
Positive
An = [In(n)]ª,
Larger s,
larger tier
Logarithmic
In(n)
Power
[In(n)]1/2
and 1/an
2n
e.g. an = C + 0, an = (-1)", an =
Both
An
Bounded
are bounded
n +1
Negative
Logarithmic
an = [In(n)]®,
s < 0
Larger s,
larger tier
[In(n)]¬1/2
1/ In(n)
±an
n=1
[In(n)]-2
1//n
Power
Diverges Or
Converges
Conditionally*
Negative
Power
Larger s,
larger tier
An = n°,
Twilight Realm*
1.0000001
-2
п
lim an = 0
(1/2)"
e-n
Exponentially
Small
Larger |q|,
larger tier
an = q",
An
0 < [q| < 1
1/(-3)"
n=1
Converges
Absolutely
Super
Small
Two examples
an = e" /n!
N/A
among many
ат, — п
Zero
Smallest](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F323bffaa-94be-44c8-ba1b-7dd55f8b7e7e%2F64cb8a1f-d61e-4ef1-a70a-10f8446d1490%2Fu30cgdk.png&w=3840&q=75)
Transcribed Image Text:Subtiers or
Series
Limit Type
Tier
Expression
Notes
Examples
Convergence
Two examples
Super
Large
an = n"
N/A
among many
An = n!
т"
3n
Exponentially
Large
Am = q",
lq| > 1
Larger |q|,
larger tier
en
(-2)"
(3/2)"
ne
lim an = ∞
n2
n=1
An = n°,
s > 0
Larger s,
larger tier
Positive
Power
Diverges
Vn
n?/3
[In(n)]?
Positive
An = [In(n)]ª,
Larger s,
larger tier
Logarithmic
In(n)
Power
[In(n)]1/2
and 1/an
2n
e.g. an = C + 0, an = (-1)", an =
Both
An
Bounded
are bounded
n +1
Negative
Logarithmic
an = [In(n)]®,
s < 0
Larger s,
larger tier
[In(n)]¬1/2
1/ In(n)
±an
n=1
[In(n)]-2
1//n
Power
Diverges Or
Converges
Conditionally*
Negative
Power
Larger s,
larger tier
An = n°,
Twilight Realm*
1.0000001
-2
п
lim an = 0
(1/2)"
e-n
Exponentially
Small
Larger |q|,
larger tier
an = q",
An
0 < [q| < 1
1/(-3)"
n=1
Converges
Absolutely
Super
Small
Two examples
an = e" /n!
N/A
among many
ат, — п
Zero
Smallest
Transcribed Image Text:With the help of the "tierlist", sort the following sequences in descending order:
dn
(-1)" + 3/In(n)
bn
n' +n-"
An
Сп
en
fn
In
п
e" — (-4)" | т" sin(-n) + (-1)"
п-е
е—п
u-
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