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Can anyone explain to me why the asymptotic relation between a function and a power series is defined in such a way:

For all N,

[tex]

f(x) - \sum_{n=0}^N a_n(x-x_0)^n << (x-x_0)^N

[/tex]

How does this incorporate the idea of asymptoticity?

Please kindly help.

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# Definition of asymptotic relation

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