An approximation for exponential.

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Homework Help Overview

The discussion revolves around finding an approximation for the expression exp(-k*L) where L is large but finite. The subject area includes concepts from calculus and series approximations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the behavior of the function as L increases, questioning the validity of using limits for approximation. There is also discussion about the applicability of power series and the necessity of considering the entire series for accurate results.

Discussion Status

The discussion is active, with participants raising questions about assumptions regarding k and the implications of using limits versus series expansions. Some guidance has been offered regarding the use of power series, though there is recognition of its limitations in this context.

Contextual Notes

Participants note that L is large but finite and that k is positive, which may influence the nature of the approximations being considered.

Alta
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Is there an approximation for exp(-k*L) with L large but finite??
 
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Well, what is
\lim_{L \to +\infty} e^{-kL}​
? Doesn't calculus tell you that limit would be a good approximation?

(P.S. are you making any assumptions about k? )
 
L is large but finite. No assumptions about k but it is positive.
 
Power series. Use as many terms as you like to improve accuracy.
I can't seem to do Latex code, but you'll find it here about a screenfull down.
http://en.wikipedia.org/wiki/Power_series

Oops - no good for negative exponent!
 
The trouble with that is that you can not say that exp(-k*L)=1+-k*L. you need the entire sum.
 

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