
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
November 29th, 2016, 10:00 AM  #1 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0 
The solution to a question states the following as s tends to 0. $\displaystyle h(s) = \frac{1e^{as}}{as 1+e^{as}}$ (1) $\displaystyle h(s) = \frac{as +o(s)}{0.5a^2s^2 + o(s^2)} $ (2) $\displaystyle h(s) approx = \frac{2}{as}$ I don't really understand how they go from step 1 to step 2. To me it seems that as s tends to 0, the top part of the equation just tends to 0? Last edited by skipjack; November 29th, 2016 at 10:29 PM. 
November 29th, 2016, 10:24 AM  #2 
Senior Member Joined: Mar 2015 From: New Jersey Posts: 1,432 Thanks: 105 
2) is from Maclaurin series. Keeping only terms in s, h(s)=h(0)+h'(0)s 
November 29th, 2016, 01:45 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,582 Thanks: 610 
$\displaystyle 1e^{as}=11+as+o(as)$ $\displaystyle as1+e^{as}=as1+1as+\frac{(as)^2}{2}+o((as)^2)$ 
November 30th, 2016, 12:00 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,511 Thanks: 1743 
WA gives $\displaystyle h(s) = \frac{2}{as}  \frac13 + \frac{as}{18}  \frac{a^2s^2}{270}  \,.\,.\,. $

December 1st, 2016, 11:37 AM  #5 
Senior Member Joined: Feb 2015 From: london Posts: 121 Thanks: 0 
Thanks all, that clears it up for me


Tags 
approximation, equation, variable 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Differential equation approximation  benmuskler  Differential Equations  1  October 17th, 2012 08:06 AM 
2 Variable Equation  dpwheelwright  Algebra  5  August 19th, 2012 12:48 AM 
Functional Equation with one variable  Phatossi  Algebra  2  March 19th, 2012 08:44 PM 
isolate a variable in this equation  superbigio  Complex Analysis  1  July 17th, 2007 03:44 PM 
Differential equation approximation  benmuskler  Differential Equations  1  December 31st, 1969 04:00 PM 