My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 18th, 2016, 04:44 PM   #1
Newbie
 
Joined: Oct 2016
From: San Francisco

Posts: 4
Thanks: 0

How do you determine the sequence is bounded above or bounded below?

Given a calculus sequence, how to find if the function is bounded above or below?
samdon123 is offline  
 
November 20th, 2016, 05:39 PM   #2
Newbie
 
Joined: Nov 2016
From: New Zealand

Posts: 1
Thanks: 0

When you have the graph, it's easier. If the function exists on the point you're looking at, and the line's coming from above, then it's bounded from above. And vice versa.
KiwiEnt is offline  
November 21st, 2016, 10:41 AM   #3
Math Team
 
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

No, one can answer this question in general, how you do that depends strongly upon the given series! For example, if the sequence were , the first thing I notice is that all numbers are positive so 0 is a lower bound. Further, this is a fraction with numerator n-1 and denominator n+ 1. Obviously n-1< n+ 1 so the numerator is always less than the denominator. That means the fraction is always less than 1 and 1 is an upper bound.
Country Boy is offline  
November 21st, 2016, 10:59 AM   #4
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,202
Thanks: 1157

Quote:
Originally Posted by Country Boy View Post
No, one can answer this question in general, how you do that depends strongly upon the given series! For example, if the sequence were $\frac{n- 1}{n+1}$, the first thing I notice is that all numbers are positive so 0 is a lower bound. Further, this is a fraction with numerator n-1 and denominator n+ 1. Obviously n-1< n+ 1 so the numerator is always less than the denominator. That means the fraction is always less than 1 and 1 is an upper bound.
changed LaTex tag as [tex] server seems down
romsek is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
bounded, determine, sequence



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Is this sequence bounded? Ganesh Ujwal Real Analysis 3 January 12th, 2015 07:36 PM
Bounded Sequence aaron-math Real Analysis 11 January 19th, 2013 10:34 AM
Show that sequence is bounded Vasily Calculus 4 June 2nd, 2012 06:46 AM
Every totally bounded set in a metric space is bounded Pintosp Real Analysis 2 April 21st, 2012 02:56 PM
proving if a sequence is bounded.. nappysnake Calculus 6 November 28th, 2011 02:39 PM





Copyright © 2018 My Math Forum. All rights reserved.