How do I carry out an approximation for this equation?(if L Ns then what?)

In summary, an approximation for an equation is a simplified or estimated solution that is close enough to the exact solution. To carry out an approximation, various methods such as linearization, truncation, or numerical methods like Taylor series or Monte Carlo simulations can be used. The importance of approximating an equation lies in finding a solution that is close enough to the exact solution, simplifying complex equations, and making them more manageable. However, an approximation can never be as accurate as the exact solution. In the context of carrying out an approximation for an equation, "L Ns then what" could refer to a specific condition or constraint that needs to be considered in the approximation process.
  • #1
Raziel2701
128
0
[itex]\frac{Ns-L}{L+Ns}[/itex]

What does that reduce to if L << Ns ? Obviously setting L to zero leads me nowhere since that argument above is actually inside a logarithm. I don't know how to perform the approximation. And the answer can't be zero by the way. Is there something I can do here? Usually the only approximations I've done before are just expansions but this is already expanded.

Thank you.
 
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  • #2
You can write it as
$$\frac{1 - L/N_s}{1 + L/N_s}$$
and then use the Binomial theorem on ##(1 + L/N_s)^{-1}##.
 

1. What is an approximation for an equation?

An approximation for an equation is a simplified or estimated solution that is close enough to the exact solution. It is often used when the exact solution is difficult or impossible to find.

2. How do I carry out an approximation for an equation?

To carry out an approximation for an equation, you can use various methods such as linearization, truncation, or numerical methods like Taylor series or Monte Carlo simulations. The method used depends on the complexity of the equation and the level of accuracy needed.

3. What is the importance of approximating an equation?

Approximating an equation allows us to find a solution that is close enough to the exact solution, which can be useful in practical applications where the exact solution is not necessary. It also helps to simplify complex equations and make them more manageable.

4. Can an approximation be as accurate as the exact solution?

No, an approximation can never be as accurate as the exact solution. However, with the use of more advanced methods and techniques, the accuracy of the approximation can be improved.

5. What does "L Ns then what" mean in the context of carrying out an approximation for an equation?

In the context of carrying out an approximation for an equation, "L Ns then what" could refer to a specific condition or constraint that needs to be considered in the approximation process. It is important to carefully examine and understand the given equation and any associated conditions before carrying out an approximation.

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