If ,

(i) find the Maclaurin’s series of f(x) up to and including the term in .

(ii) Hence deduce the series expansion of the function up to and including the term in

**Solution**

(i) is routine, can easily work out to be

(ii) requires Higher Order Thinking (HOT)

We differentiate the series obtained in (i) to get

Principle used: Differentiate one series expansion to get the series expansion for another series.

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