9 Let \(\mathrm { f } ( x ) = \frac { 14 - 3 x + 2 x ^ { 2 } } { ( 2 + x ) \left( 3 + x ^ { 2 } \right) }\).
- Express \(\mathrm { f } ( x )\) in partial fractions.
- Hence obtain the expansion of \(\mathrm { f } ( x )\) in ascending powers of \(x\), up to and including the term in \(x ^ { 2 }\).
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The diagram shows a trapezium \(A B C D\) in which \(A D = B C = r\) and \(A B = 2 r\). The acute angles \(B A D\) and \(A B C\) are both equal to \(x\) radians. Circular arcs of radius \(r\) with centres \(A\) and \(B\) meet at \(M\), the midpoint of \(A B\).