2023 TJC P1 Q3

The function \(\mathrm{g}\) is defined by

\(\mathrm{g}\left( x \right)=\frac{x}{\sqrt{4-x}}\), \(x\in \mathbb{R}\), \(0 < x < 4\).

It is given that \(\mathrm{f}\left( x \right)=ax+b{{x}^{2}}+c{{x}^{3}}\) is the binomial expansion of \(\mathrm{g}\left( x \right)=\frac{x}{\sqrt{4-x}}\) in ascending powers of \(x\) up to and including terms in \({{x}^{3}}\).

1. Find the exact value of \(a\), \(b\) and \(c\).[4]
2. Find the range of values of \(x\) such that the percentage error in using \(\mathrm{f}\left( x \right)\) to approximate \(\mathrm{g}\left( x \right)\) is less than \(4\%\).[2]