An approximation for exponential.

AI Thread Summary
An approximation for exp(-k*L) when L is large but finite is under discussion, with the limit as L approaches infinity suggesting a useful approximation. The conversation highlights that while calculus provides insights, the approximation must consider the entire power series rather than truncating it to the first few terms. It is noted that negative exponents complicate the use of simple approximations, as the full series expansion is necessary for accuracy. The discussion emphasizes that k is assumed to be positive, which influences the behavior of the function. Overall, a comprehensive approach using power series is recommended for better accuracy in approximating the exponential function.
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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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