4.
$$\mathrm { f } ( x ) = \sqrt { 1 - 4 x ^ { 2 } } \quad | x | < \frac { 1 } { 2 }$$
- Find, in ascending powers of \(x\), the first four non-zero terms of the binomial expansion of \(\mathrm { f } ( x )\). Give each coefficient in simplest form.
- By substituting \(x = \frac { 1 } { 4 }\) into the binomial expansion of \(\mathrm { f } ( x )\), obtain an approximation for \(\sqrt { 3 }\)
Give your answer to 4 decimal places.
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