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[SOLVED] Taylor approximation
I have an exact funktion given as:
[tex]P(r)=1-e^{\frac{-2r}{a}}(1+\frac{2r}{a}+\frac{2r^2}{a^2})[/tex]
I need to prove, by making a tayler series expansion, that:
[tex]P(r)\approx \frac{3r^3}{4a^4}[/tex]
When [tex]r \prec \prec a[/tex]
I am lost when it comes to these Taylor approximations. It should be a fairly easy problem, but don't know how to handle it.
Some help on how to do this would be appreciated.
Homework Statement
I have an exact funktion given as:
[tex]P(r)=1-e^{\frac{-2r}{a}}(1+\frac{2r}{a}+\frac{2r^2}{a^2})[/tex]
I need to prove, by making a tayler series expansion, that:
[tex]P(r)\approx \frac{3r^3}{4a^4}[/tex]
When [tex]r \prec \prec a[/tex]
The Attempt at a Solution
I am lost when it comes to these Taylor approximations. It should be a fairly easy problem, but don't know how to handle it.
Some help on how to do this would be appreciated.