My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
May 22nd, 2018, 04:49 AM   #1
Newbie
 
Joined: Jul 2017
From: KOLKATA

Posts: 29
Thanks: 2

limit of Mod functions

lim |x|/x as x->infinity

I Think this should be = 1 as this is indeterminate form and we can apply L Hospitals Rule . But the text book answer says that limit does not exist . which one is correct
arybhatta01 is offline  
 
May 22nd, 2018, 05:09 AM   #2
Senior Member
 
Joined: Aug 2017
From: United Kingdom

Posts: 211
Thanks: 64

Math Focus: Algebraic Number Theory, Arithmetic Geometry
You're right that the limit as x tends to infinity is 1. (But you really don't need L'Hospital to see this. Just plot the graph of this function: it takes the value 1 for all x > 0 and the value -1 for all x < 0.)

I suspect the book meant to ask about the limit as x tends to zero, in which case it's correct in saying there is no limit. Indeed, it has distinct left and right limits at 0 (1 and -1).
cjem is offline  
May 22nd, 2018, 05:42 AM   #3
Newbie
 
Joined: Jul 2017
From: KOLKATA

Posts: 29
Thanks: 2

But since x tends to infinity x < 0 will not come into picture . So limit is always 1 . Am I correct ?
arybhatta01 is offline  
May 22nd, 2018, 05:44 AM   #4
Newbie
 
Joined: Jul 2017
From: KOLKATA

Posts: 29
Thanks: 2

I agree limit will not exist if x tends to 0
arybhatta01 is offline  
May 22nd, 2018, 06:11 AM   #5
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,342
Thanks: 2463

Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by arybhatta01 View Post
But since x tends to infinity x < 0 will not come into picture . So limit is always 1 . Am I correct ?
Yes.

Whenever dealing with $|f(X)|$, you first determine whether $f(x)=0$ zero within the interval of interest. If it does, split the interval at all such points and consider subintervals separately.

Then for each (sub-)interval simply replace $|f(x)|$ with either $f(x)$ or $-f(x)$ as appropriate.
v8archie is online now  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
functions, limit, mod



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
The Limit of Functions Calc Calculus 3 March 13th, 2015 02:01 PM
Sum of two functions doesn't exceed limit Dario Real Analysis 1 April 5th, 2014 11:17 AM
Limit and infinitesimal functions Ockonal Calculus 11 November 30th, 2011 12:57 PM
Proving the limit of the quotient of two functions? mfetch22 Calculus 3 August 25th, 2010 07:41 AM
The limit of a series of functions elim Real Analysis 2 August 18th, 2010 10:10 PM





Copyright © 2018 My Math Forum. All rights reserved.