1 The first three terms, in ascending powers of \(x\), of the binomial expansion of \(( 9 + 2 x ) ^ { \frac { 1 } { 2 } }\) are given by
$$( 9 + 2 x ) ^ { \frac { 1 } { 2 } } \approx a + \frac { x } { 3 } - \frac { x ^ { 2 } } { 54 }$$
where \(a\) is a constant.
1
- State the range of values of \(x\) for which this expansion is valid.
Circle your answer.
\(| x | < \frac { 2 } { 9 }\)
\(| x | < \frac { 2 } { 3 }\)
\(| x | < 1\)
\(| x | < \frac { 9 } { 2 }\)
1 - Find the value of \(a\).
Circle your answer.
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[1 mark]
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