My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


Thanks Tree2Thanks
  • 1 Post By greg1313
  • 1 Post By skeeter
Reply
 
LinkBack Thread Tools Display Modes
April 29th, 2017, 09:39 AM   #1
Senior Member
 
Joined: Feb 2015
From: london

Posts: 121
Thanks: 0

Function tends to

If I have the function:

$\displaystyle w = \frac{y}{u^2 (1-e^{-y/u})}$

If y is MUCH smaller than u, could you argue that w = 1/u.

***Disclaimer*** I may well have calculated w wrong which is why I cant seem to argue that w tends to 1/u
calypso is offline  
 
April 29th, 2017, 10:57 AM   #2
Global Moderator
 
greg1313's Avatar
 
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,638
Thanks: 959

Math Focus: Elementary mathematics and beyond
$$\lim_{y\to0}\frac{y}{u^2(1-e^{-y/u})}=\frac1u$$
Thanks from calypso
greg1313 is offline  
April 29th, 2017, 02:01 PM   #3
Senior Member
 
Joined: Feb 2015
From: london

Posts: 121
Thanks: 0

thanks for the quick reply. If its easy to explain, do you mind expanding a little on why that is the case. I can see that when u >> y, $\displaystyle w -> y/u^2$. But I dont understand how u^2 -> u
calypso is offline  
April 29th, 2017, 02:55 PM   #4
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,656
Thanks: 1327

$\displaystyle \dfrac{1}{u^2} \lim_{y \to 0} \dfrac{y}{1 - e^{-y/u}}$

L'Hopital ...

$\displaystyle \dfrac{1}{u^2} \lim_{y \to 0} \dfrac{1}{\left(-\frac{1}{u}\right)\left(-e^{-y/u}\right)}$

$\displaystyle \dfrac{1}{u^2} \lim_{y \to 0} \dfrac{u}{e^{-y/u}} = \dfrac{1}{u^2} \cdot \dfrac{u}{1} = \dfrac{1}{u}$
Thanks from calypso
skeeter is offline  
April 29th, 2017, 03:07 PM   #5
Senior Member
 
Joined: Feb 2015
From: london

Posts: 121
Thanks: 0

thanks again, very clear explanation
calypso is offline  
Reply

  My Math Forum > High School Math Forum > Elementary Math

Tags
approx, function



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
guessing the base function of a real function that meets certain requirements vlekje5 Pre-Calculus 11 March 27th, 2017 01:58 PM
Finding a probability density function from a distribution function and using it. Rramos2 Advanced Statistics 5 February 11th, 2017 12:38 PM
Inverting the Riemann Zeta Function with the Mobius Function neelmodi Number Theory 0 February 4th, 2015 10:52 AM
Derivation of tau function, sigma, euler and mobius function msgelyn Number Theory 2 January 12th, 2014 04:13 AM
Find all linear function given a function equals its inverse deSitter Algebra 4 April 10th, 2013 02:17 PM





Copyright © 2017 My Math Forum. All rights reserved.