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I already learn to use Taylor series as:

f(x) = ∑ f

But i don´t see why the serie change when we use differents x

Por example:

f(x) = x

to express Taylor series in x

f(x) = f(0) + f(0) (x-0) + ..... = 0 due to f(0) = (0)

to x

f(x) = 1 + 2(x-1) + (x-1)

Why happens this?

and, when we use the Taylor series, which situations we said that we can despreciate some terms, like cuadratic terms?

f(x) = ∑ f

^{n}(x_{0}) / n! (x-x_{0})^{n}But i don´t see why the serie change when we use differents x

_{0}points.Por example:

f(x) = x

^{2}to express Taylor series in x

_{0}= 0f(x) = f(0) + f(0) (x-0) + ..... = 0 due to f(0) = (0)

^{2}to x

_{0}=1 the series are totally differentsf(x) = 1 + 2(x-1) + (x-1)

^{2}this is the parabolaWhy happens this?

and, when we use the Taylor series, which situations we said that we can despreciate some terms, like cuadratic terms?

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