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I've never really studied various ways of expanding expressions in order to obtain an approximation that can make calculations easier. For example,

[tex]

p^t = \frac{m}{\sqrt{1 - v^2}}

[/tex]

reduces to

[tex]

p^t = m + \frac{1}{2}mv^2 + ...

[/tex]

for v << 1.

How does one arrive at something like this? What other expansions are useful? I used to think that I'd just calculate everything exactly but I now realize these sorts of expansions are extremeley important.

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# Aproximations by Expansion

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