Problem

$$\mathrm{g}(x)=\frac{1}{\sqrt{4-x^2}}$$

(a) 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.

(b) State the range of values of $x$ for which this expansion is valid.

(c) Use the expansion from part (a) to find a fully simplified rational approximation for $\sqrt{3}$

Show your working and make your method clear.