11. a. Find the binomial expansion of \(( 4 - x ) ^ { - \frac { 1 } { 2 } }\), up to and including the term in \(x ^ { 2 }\). Given that the binomial expansion of \(\mathrm { f } ( x ) = \sqrt { \frac { 1 + 2 x } { 4 - x } } , | x | < \frac { 1 } { 4 }\), is $$\frac { 1 } { 2 } + \frac { 9 } { 16 } x - A x ^ { 2 } + \cdots$$ b. Show that the value of the constant \(A\) is \(\frac { 45 } { 256 }\)
c. By substituting \(x = \frac { 1 } { 4 }\) into the answer for (b) find an approximate for \(\sqrt { 10 }\), giving your answer to 3 decimal places.