My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
November 18th, 2013, 06:03 PM   #1
Senior Member
 
stainburg's Avatar
 
Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

In what situation frac of limits equals to limit of frac?

I mean
,
or
stainburg is offline  
 
November 18th, 2013, 06:12 PM   #2
Senior Member
 
stainburg's Avatar
 
Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: In what situation frac of limits equals to limit of fr

Of course, we have to suppose that limit of g(x) exists when x goes to a rational number 'a' or infinity but it never goes to zero!
stainburg is offline  
November 18th, 2013, 06:29 PM   #3
Senior Member
 
stainburg's Avatar
 
Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: In what situation frac of limits equals to limit of fr

A Chinese physicist argued with me days ago.
He believes that .
I said :"you're freakin me out, because any mathematical analysis textbook will never ever teach that. is indetermined, and you can never tell how fast the x's in numerator and denominator go to infinity!"
Of course, as he said, I go to hell
stainburg is offline  
November 18th, 2013, 07:49 PM   #4
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,882
Thanks: 1088

Math Focus: Elementary mathematics and beyond
Re: In what situation frac of limits equals to limit of fr



The limit laws aren't much help in determining the limit but I believe what he says is correct.

I'm sure there is a warm spot for me down there as well.
greg1313 is offline  
November 18th, 2013, 08:26 PM   #5
Senior Member
 
stainburg's Avatar
 
Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: In what situation frac of limits equals to limit of fr

Quote:
Originally Posted by greg1313


The limit laws aren't much help in determining the limit but I believe what he says is correct.

I'm sure there is a warm spot for me down there as well.
If g(n) is a Cauchy sequence and we taking it as the denominator that never goes to zero, I believe the conclusion is true. Cuz the limit operation results to a real number.But infinity divides infinity, seriously?
stainburg is offline  
November 18th, 2013, 11:13 PM   #6
Senior Member
 
Joined: Feb 2013

Posts: 281
Thanks: 0

Re: In what situation frac of limits equals to limit of fr

f(x): R --> R
g(x): R --> R

1) Suppose there is an epsilon such that g(x)<>0 if x in (a-epsion,a+epsilon) interval and and lim g(x)<>0. Then
f converges to a real number <--> lim f / lim g = lim f/g.
f diverges to +inf <--> f/g diverges to +inf
f divergent <--> f/g divergent

2) Suppose there is an epsilon such that g(x)<>0 if x in (a-epsion,a+epsilon) interval and lim g(x)=0.
Then lim f/g can exist and can not exist, can converge to any real number or to +/-inf.
lim f / lim g is undefined, becasuse divived by zero.

3) Suppose lim f = lim g = + inf. Then lim f/g can exist or can not exist. Lim f/g can converge to +inf or any non-negative real, but not to negative real.
lim f / lim g is undefined, becasuse division is defined (by definition) on real numbers.
An example when lim f/g doesn't exist:
g(x) = 1/abs(x-a)
f(x) = 1/abs(x-a) if x is rational, 2/abs(x-a) if x is irrational




Quote:
Again, inf/inf doesn't make sense regarding as a fraction, because you can only divide a real number by a real number. Therefore the equation (the first) is incorrect.
csak is offline  
November 19th, 2013, 01:48 PM   #7
Math Team
 
Joined: Sep 2007

Posts: 2,409
Thanks: 6

Re: In what situation frac of limits equals to limit of fr

Quote:
Originally Posted by stainburg
A Chinese physicist argued with me days ago.
He believes that .
I said :"you're freakin me out, because any mathematical analysis textbook will never ever teach that. is indetermined, and you can never tell how fast the x's in numerator and denominator go to infinity!
Of course, as he said, I go to hell
Then you do not know what "undetermined" (or "indeterminate") means. has both numerator and denominator going to infinity so is "indeterminate". But it should be obvious, even to you, that .
HallsofIvy is offline  
November 19th, 2013, 03:14 PM   #8
Senior Member
 
stainburg's Avatar
 
Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: In what situation frac of limits equals to limit of fr

Quote:
Originally Posted by HallsofIvy
Then you do not know what "undetermined" (or "indeterminate") means. has both numerator and denominator going to infinity so is "indeterminate". But it should be obvious, even to you, that .
So, you suppose me never go to the college. What would you call infinity/infinity?
stainburg is offline  
November 19th, 2013, 04:00 PM   #9
Senior Member
 
stainburg's Avatar
 
Joined: Oct 2010
From: Changchun, China

Posts: 492
Thanks: 14

Re: In what situation frac of limits equals to limit of fr

Quote:
Originally Posted by csak
Again, inf/inf doesn't make sense regarding as a fraction, because you can only divide a real number by a real number. Therefore the equation (the first) is incorrect.
Thanks for the answer. I believe inf/inf doesn't make sense, too. Another question: how about DiracDelta(0)/DiracDelta(0) ? This truly confuses me
stainburg is offline  
November 19th, 2013, 06:35 PM   #10
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,372
Thanks: 233

Re: In what situation frac of limits equals to limit of fr

What if you do this ?





Since



agentredlum is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
equals, frac, limit, limits, situation



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
prove this limit equals 0 yogazen2013 Calculus 2 October 5th, 2013 09:44 AM
Showing limit equals derivative jpanderson8 Calculus 1 September 26th, 2013 10:45 AM
find [latex]/frac{dy}{dx}[/latex] sivela Calculus 1 April 26th, 2010 05:53 PM
...and still. trouble with complex frac. in limit problem oddlogic Linear Algebra 6 January 29th, 2010 09:55 AM
frac(e^n) Yegreg Number Theory 1 December 3rd, 2007 08:33 PM





Copyright © 2018 My Math Forum. All rights reserved.