4.
$$g ( x ) = \frac { 1 } { \sqrt { 4 - x ^ { 2 } } }$$
- Find, in ascending powers of \(x\), the first four non-zero terms of the binomial expansion of \(\mathrm { g } ( x )\). Give each coefficient in simplest form.
- State the range of values of \(x\) for which this expansion is valid.
- Use the expansion from part (a) to find a fully simplified rational approximation for \(\sqrt { 3 }\)
Show your working and make your method clear.