determine, in simplest form, \(\frac { \mathrm { d } ^ { 3 } y } { \mathrm {~d} x ^ { 3 } }\)
Hence determine the Maclaurin series expansion of \(\ln ( 5 + 3 x )\), in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), giving each coefficient in simplest form.
Hence write down the Maclaurin series expansion of \(\ln ( 5 - 3 x )\), in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), giving each coefficient in simplest form.
Use the answers to parts (b) and (c) to determine the first 2 non-zero terms, in ascending powers of \(x\), of the Maclaurin series expansion of
$$\ln \left( \frac { 5 + 3 x } { 5 - 3 x } \right)$$