An approximation for exponential.

In summary, for large but finite values of L and a positive value of k, we can use a power series with as many terms as desired to approximate the value of exp(-k*L). However, this method may not be applicable for negative values of the exponent. Calculus can also be used to determine the limit of exp(-k*L) as L approaches infinity, which can also serve as a good approximation.
  • #1
Alta
13
0
Is there an approximation for exp(-k*L) with L large but finite??
 
Physics news on Phys.org
  • #2
Well, what is
[tex]\lim_{L \to +\infty} e^{-kL}[/tex]​
? Doesn't calculus tell you that limit would be a good approximation?

(P.S. are you making any assumptions about k? )
 
  • #3
L is large but finite. No assumptions about k but it is positive.
 
  • #4
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!
 
  • #5
The trouble with that is that you can not say that exp(-k*L)=1+-k*L. you need the entire sum.
 

1. What is an approximation for exponential?

An approximation for exponential is a method for estimating the value of an exponential function without having to calculate it exactly. It is a simplified version of the original function that is close enough to the actual value for practical use.

2. How is an approximation for exponential useful?

An approximation for exponential is useful in situations where the exact value of an exponential function is difficult or time-consuming to calculate. It allows for quick estimations and can be used to simplify complex calculations.

3. What are the different types of approximations for exponential?

There are several types of approximations for exponential, including linear approximations, Taylor series approximations, and Padé approximations. Each type has its own advantages and is used in different contexts.

4. How accurate are approximations for exponential?

The accuracy of an approximation for exponential depends on the type of approximation used and the degree of approximation. Generally, the more complex the method, the more accurate the approximation will be. However, even simple approximations can provide reasonably accurate results.

5. How do I choose the best approximation for my needs?

The best approximation for exponential will depend on the specific situation and the desired level of accuracy. It is important to consider the simplicity and computational efficiency of the approximation method, as well as its accuracy, when choosing the best option for your needs.

Similar threads

  • Introductory Physics Homework Help
Replies
5
Views
328
  • Introductory Physics Homework Help
Replies
6
Views
993
  • Introductory Physics Homework Help
Replies
20
Views
1K
Replies
2
Views
247
  • Introductory Physics Homework Help
Replies
2
Views
764
  • Introductory Physics Homework Help
Replies
2
Views
814
  • Introductory Physics Homework Help
Replies
3
Views
838
  • Introductory Physics Homework Help
Replies
4
Views
580
  • Introductory Physics Homework Help
Replies
29
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
817
Back
Top