Problem

Find the limit of the sequence $ \left\{ \sqrt 2…

02:20

Problem 78 Medium Difficulty

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
$ a_n = n^3 - 3n + 3 $

Answer

Monotonic but not bounded

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Discussion

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Video Transcript

first, let's determine whether it's increasing or decreasing. So here, what we can do is just replace this with the function f of X By replacing all the ends with ex. Now we have f prime of X equals three X squared minus three, and this is bigger than her equal to zero. If X is bigger than or equal to one, so F is increasing. Therefore, a N is increasing there and which implies that it's monotonic. So that's the first part of this question increasing. And it is monotonic. The next question is, is the sequence bounded? Well, notice that the limit as n goes to infinity of a n equals the limit. X goes to infinity. F of X equals infinity. So this means that a N is not bounded since it's not bounded above, so not bounded. But it is monotone increasing, and that's our final answer

J H.

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Problem

Find the limit of the sequence $ \left\{ \sqrt 2…

Problem 78 Medium Difficulty

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
$ a_n = n^3 - 3n + 3 $

Answer

Monotonic but not bounded

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Catherine R.

Anna Marie V.

Kayleah T.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Catherine R.

Anna Marie V.

Kayleah T.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

Find the limit of the sequence $ \left\{ \sqrt 2…

Problem 78 Medium Difficulty

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?$ a_n = n^3 - 3n + 3 $

Answer

Monotonic but not bounded

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Catherine R.

Anna Marie V.

Kayleah T.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Catherine R.

Anna Marie V.

Kayleah T.

Kristen K.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Determine whether the sequence is increasing, decreasing, or not monotonic. Is the sequence bounded?
$ a_n = n^3 - 3n + 3 $