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16.2 Taylor polynomial[2D2]

Definition 34 Landau Symbols

[1FB]

In the following for simplicity we consider only the case in which \(\lim _{x→ a}g(x)=0\); moreover in Taylor’s expansion we always have that \(g(x)=(x-a)^ n\) with \(n≥ 1\) integer. 1

Remark 35

[1FC]

Let’s see two examples. Let \(a=0\) for simplicity.

Example 36

[1FD]

Example 37

[1FF]

E37

[1FG]

E37

[1FJ]

E37

[1FM]

E37

[1FP]

E37

[1FR]

E37

[1FT]

QuasiEsercizio 49

[1FW]

See also exercise [1BR].

  1. Some authors also use the \(o(1)\) notation to indicate an infinitesimal quantity for \(x→ a\), but this can generate confusion .
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  • Taylor's theorem
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