My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 8th, 2013, 01:04 AM   #1
Senior Member
 
Joined: Jul 2012

Posts: 225
Thanks: 0

Can I apply L'hopital here?

hi all



Can i apply lhopital when the limit of the numerator is different than the denominator but both are infinite?
OriaG is offline  
 
February 8th, 2013, 02:24 AM   #2
Member
 
chocolatesheep's Avatar
 
Joined: Jul 2012

Posts: 60
Thanks: 0

Math Focus: Calculus
Re: Can I apply L'hopital here?

I think so. However, I've been wrong about this before so I'm going to give you an alternative here. My teacher never taught us Lhopitals rule. She took a different approach.
She drew the graphs of the following functions: y=ln(x); y=sqrt(x); y=x^2; y=e^x as an example. Then we looked at the graphs and saw that as x aproaches infinity all these functions approach infinity.
But ln(x) approaches infinity the slowest. If you draw it you will see the function (y=ln(x)) grows very slowly compared to y=sqrt(x). So y=ln(x) approaches infinity a lot slower than y = sqrt(x)
So we ranked these functions based on how fast they grow when x->infinity.
y=ln(x) is the slowest, followed by y=sqrt(x) then y=x, after that goes y=x^2 (or x^n) and the fastest growing function is y=e^x (or a^x where a>1)
But this only applies when x->infinity, not when x->0 or any other number.



we can say 1/x = t, so the the limit becomes the following:





as t-> infinity ln(t) grows slower, and t grows faster therefor we have a smaller infinity divided by a bigger infinity and so we will get 0






We can also try to do it with L'Hopitals rule:













So yes you can do it with L'Hopitals rule
chocolatesheep is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
apply, lhopital



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
De Moivre's formula apply here? WWRtelescoping Complex Analysis 2 March 2nd, 2014 11:13 PM
What is the correct way to apply quadratic formula? king.oslo Algebra 9 February 13th, 2013 07:02 AM
How to Apply the Shapley Value Formula? Aqil Economics 0 December 14th, 2012 12:31 PM
what are the limit questions whic you can't apply L'hopital' silvercats Calculus 5 June 26th, 2011 06:24 AM
Why does this apply to all tables except to a multiple of 3? DragonsMath Calculus 2 November 19th, 2010 08:34 AM





Copyright © 2018 My Math Forum. All rights reserved.