9. (i) Use the binomial expansion to show that \(( 1 - 2 x ) ^ { - \frac { 1 } { 2 } } \approx 1 + x + \frac { 3 } { 2 } x ^ { 2 }\) for sufficiently small values of \(x\).
(ii) For what values of \(x\) is the expansion valid?
(iii) Find the expansion of \(\sqrt { \frac { 1 + 2 x } { 1 - 2 x } }\) in ascending powers of \(x\) as far as the term in \(x ^ { 2 }\).
(iv) Use \(x = \frac { 1 } { 20 }\) in your answer to part (iii) to find an approximate value for \(\sqrt { 11 }\).
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