Challenging Maclaurin’s series problem 1

If Tex2Img_1402896309,

(i) find the Maclaurin’s series of f(x) up to and including the term in Tex2Img_1402896490.

(ii) Hence deduce the series expansion of the function Tex2Img_1402896783 up to and including the term in Tex2Img_1402896839

Solution

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

Tex2Img_1402896636

(ii) requires Higher Order Thinking (HOT)

We differentiate the series obtained in (i) to get Tex2Img_1402897125

Tex2Img_1402897294

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

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