2.
$$f ( x ) = \frac { 3 } { \sqrt { 1 - x } } , | x | < 1$$
- Show that \(\mathrm { f } \left( \frac { 1 } { 10 } \right) = \sqrt { 10 }\).
- Expand \(\mathrm { f } ( x )\) in ascending powers of \(x\) up to and including the term in \(x ^ { 3 }\), simplifying each coefficient.
- Use your expansion to find an approximate value for \(\sqrt { 10 }\), giving your answer to 8 significant figures.
- Find, to 1 significant figure, the percentage error in your answer to part (c).