- The function \(f\) is given by
$$f ( x ) = \frac { 25 x + 32 } { ( 2 x - 5 ) ( x + 1 ) ( x + 2 ) }$$
- Express \(f ( x )\) in terms of partial fractions.
- Show that \(\int _ { 1 } ^ { 2 } f ( x ) \mathrm { d } x = - \ln P\), where \(P\) is an integer whose value is to be found.
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} - Show that the sign of \(f ( x )\) changes in the interval \(x = 2\) to \(x = 3\). Explain why the change of sign method fails to locate a root of the equation \(f ( x ) = 0\) in this case.