4.
$$f ( x ) = \frac { 27 } { ( 3 - 5 x ) ^ { 2 } } \quad | x | < \frac { 3 } { 5 }$$
- Find the series expansion of \(\mathrm { f } ( x )\), in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\). Give each coefficient in its simplest form.
(5)
Use your answer to part (a) to find the series expansion in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\), of - \(g ( x ) = \frac { 27 } { ( 3 + 5 x ) ^ { 2 } } \quad | x | < \frac { 3 } { 5 }\)
- \(\mathrm { h } ( x ) = \frac { 27 } { ( 3 - x ) ^ { 2 } } \quad | x | < 3\)