Find the first five non-zero terms of power series representation centered at x=0x=0 for the function below. f(x)=ln(5−x) f(x)=ln⁡(5−x)

The first five non-zero terms of power series representation centered at are contained in .

Natural logarithms are trascendent functions and transcendent functions can be approximated by Taylor polynomials, a fifth-order Taylor polynomial is represented by the following expression:

(1)

Where is the initial point. If we know that and , then the Taylor polynomial is:

, , , ,

The first five non-zero terms of power series representation centered at are contained in .

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If , then

So the first five terms of the series expansion around are