Limit Type Tier Expression Notes Examples = n" = n! Convergence Two examples Super Large N/A among many т 3" Exponentially Large An = q", la| > 1 Larger |q|, larger tier en (-2)" (3/2)" пе lim an n2 n=1 Larger s, larger tier Positive an = n°, Power Diverges" Vn n!/3 [In(n)]² In(n) Positive An [In(n)]°, Larger s, Logarithmic larger tier Power [In(n)]/2 and 1/an 2n e.g. an = C # 0, an = (-1)", an = Both ат Bounded are bounded n +1 Negative Logarithmic [In(n)]-1/2 1/ In(n) an = [In(n)]°, Larger s, larger tier ±an Power n=1 [In(n)]-2 1/Vn Diverges Or Converges Conditionally" -1 п Larger s, larger tier Negative An = n°, Twilight Realm Power -1.0000001 п -2 lim an = 0 п—00 (1/2)" Exponentially Small an = q", 0 < ]q| < 1 Larger |q|, larger tier Σ. An 1/(-3)" n=1 Converges Absolutely -n Two examples an = e" /n! Super Small N/A among many Zero An = 0 Smallest 0. With the help of the "tierlist", sort the following sequences in descending order: b, Сп dn en In n +n (-1)" + 3/ln(n) | n' (-4)" | п" | sin(-п) + (-1)" 72 п
Limit Type Tier Expression Notes Examples = n" = n! Convergence Two examples Super Large N/A among many т 3" Exponentially Large An = q", la| > 1 Larger |q|, larger tier en (-2)" (3/2)" пе lim an n2 n=1 Larger s, larger tier Positive an = n°, Power Diverges" Vn n!/3 [In(n)]² In(n) Positive An [In(n)]°, Larger s, Logarithmic larger tier Power [In(n)]/2 and 1/an 2n e.g. an = C # 0, an = (-1)", an = Both ат Bounded are bounded n +1 Negative Logarithmic [In(n)]-1/2 1/ In(n) an = [In(n)]°, Larger s, larger tier ±an Power n=1 [In(n)]-2 1/Vn Diverges Or Converges Conditionally" -1 п Larger s, larger tier Negative An = n°, Twilight Realm Power -1.0000001 п -2 lim an = 0 п—00 (1/2)" Exponentially Small an = q", 0 < ]q| < 1 Larger |q|, larger tier Σ. An 1/(-3)" n=1 Converges Absolutely -n Two examples an = e" /n! Super Small N/A among many Zero An = 0 Smallest 0. With the help of the "tierlist", sort the following sequences in descending order: b, Сп dn en In n +n (-1)" + 3/ln(n) | n' (-4)" | п" | sin(-п) + (-1)" 72 п
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...
Related questions
Question
![Limit Type
Tier
Expression
Notes
Examples
= n"
= n!
Convergence
Two examples
Super
Large
N/A
among many
т
3"
Exponentially
Large
An = q",
la| > 1
Larger |q|,
larger tier
en
(-2)"
(3/2)"
пе
lim an
n2
n=1
Larger s,
larger tier
Positive
an = n°,
Power
Diverges"
Vn
n!/3
[In(n)]²
In(n)
Positive
An
[In(n)]°,
Larger s,
Logarithmic
larger tier
Power
[In(n)]/2
and 1/an
2n
e.g. an = C # 0, an = (-1)", an =
Both
ат
Bounded
are bounded
n +1
Negative
Logarithmic
[In(n)]-1/2
1/ In(n)
an = [In(n)]°,
Larger s,
larger tier
±an
Power
n=1
[In(n)]-2
1/Vn
Diverges Or
Converges
Conditionally"
-1
п
Larger s,
larger tier
Negative
An = n°,
Twilight Realm
Power
-1.0000001
п
-2
lim an = 0
п—00
(1/2)"
Exponentially
Small
an = q",
0 < ]q| < 1
Larger |q|,
larger tier
Σ.
An
1/(-3)"
n=1
Converges
Absolutely
-n
Two examples
an = e" /n!
Super
Small
N/A
among many
Zero
An = 0
Smallest
0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F323bffaa-94be-44c8-ba1b-7dd55f8b7e7e%2F6b0e0923-f440-44df-ad28-18ea3a560a0f%2Fhzcp1xf.png&w=3840&q=75)
Transcribed Image Text:Limit Type
Tier
Expression
Notes
Examples
= n"
= n!
Convergence
Two examples
Super
Large
N/A
among many
т
3"
Exponentially
Large
An = q",
la| > 1
Larger |q|,
larger tier
en
(-2)"
(3/2)"
пе
lim an
n2
n=1
Larger s,
larger tier
Positive
an = n°,
Power
Diverges"
Vn
n!/3
[In(n)]²
In(n)
Positive
An
[In(n)]°,
Larger s,
Logarithmic
larger tier
Power
[In(n)]/2
and 1/an
2n
e.g. an = C # 0, an = (-1)", an =
Both
ат
Bounded
are bounded
n +1
Negative
Logarithmic
[In(n)]-1/2
1/ In(n)
an = [In(n)]°,
Larger s,
larger tier
±an
Power
n=1
[In(n)]-2
1/Vn
Diverges Or
Converges
Conditionally"
-1
п
Larger s,
larger tier
Negative
An = n°,
Twilight Realm
Power
-1.0000001
п
-2
lim an = 0
п—00
(1/2)"
Exponentially
Small
an = q",
0 < ]q| < 1
Larger |q|,
larger tier
Σ.
An
1/(-3)"
n=1
Converges
Absolutely
-n
Two examples
an = e" /n!
Super
Small
N/A
among many
Zero
An = 0
Smallest
0.
Transcribed Image Text:With the help of the "tierlist", sort the following sequences in descending order:
b,
Сп
dn
en
In
n +n
(-1)" + 3/ln(n) | n'
(-4)" | п" | sin(-п) + (-1)"
72
п
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning