Considering the functions,
(i) By writing ln(2 − x) = ln 2 + ln(1 − (x/2) ), and using substitution in one of the standard Taylor series, find the Taylor series about 0 for f. Give explicitly all terms up to the term in x^3. Determine a range of validity for thisTaylor series.
(ii) Use your answer to part (i), and the fact that 6 − x = 2 − (x−4), tofind the Taylor series about 4 for g. Give explicitly the same number of terms as in part (i). Determine a range of validity for this Taylor series.
(iii) Check the first four terms in the Taylor series that you found in part (ii) by finding the first, second and third derivatives of g, and using these to find the cubic Taylor polynomial about 4 for g.
Please I'm struggling to start this exercise I have read my books but I'm not getting how the Taylor series works, maybe is because I still have found a reason for what Taylor sees is used and get bored and distracted every time I work with it.
So an easy and straight forward explanation will also be much appreciated.