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[Solution] (a) Find the first three non-zero terms of the Taylor series expansion of f(x)=x √x+1 about the point x=0. (b) Deduce from (a) how the

Question: (a) Find the first three non-zero terms of the Taylor series expansion of \(f(x)=x \sqrt{x+1}\)

about the point \(x=0\).

(b) Deduce from (a) how the \(n\) th term of the expansion looks like.

(c) Use the result in (a) to order the following functions by size, for \(x\) close to 0 :

  1. \(x \sqrt{x+1}\), (ii) \(x^{2} \sqrt{x+1}, \quad\) (iii) \(\sqrt{x+1}\).

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