3. $$f ( x ) = \frac { 27 x ^ { 2 } + 32 x + 16 } { ( 3 x + 2 ) ^ { 2 } ( 1 - x ) } , \quad | x | < \frac { 2 } { 3 }$$ Given that \(\mathrm { f } ( x )\) can be expressed in the form $$f ( x ) = \frac { A } { ( 3 x + 2 ) } + \frac { B } { ( 3 x + 2 ) ^ { 2 } } + \frac { C } { ( 1 - x ) }$$

1. find the values of \(B\) and \(C\) and show that \(A = 0\).
2. Hence, or otherwise, find the series expansion of \(\mathrm { f } ( x )\), in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\). Simplify each term.
3. Find the percentage error made in using the series expansion in part (b) to estimate the value of \(\mathrm { f } ( 0.2 )\). Give your answer to 2 significant figures. \section*{LU}