5. (a) Expand \(\sqrt { 1 + 2 x }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\).
(b) Hence expand \(\frac { \sqrt { 1 + 2 x } } { 1 + 9 x ^ { 2 } }\) in ascending powers of \(x\), up to and including the term in \(x ^ { 3 }\).
(c) Determine the range of values of \(x\) tor which the expansion in part (b) is valid.
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