16 The function f is defined by
$$f ( x ) = \frac { a x + 5 } { x + b }$$
where \(a\) and \(b\) are constants.
The graph of \(y = \mathrm { f } ( x )\) has asymptotes \(x = - 2\) and \(y = 3\)
16
- Write down the value of \(a\) and the value of \(b\)
16
- The diagram shows the graph of \(y = \mathrm { f } ( x )\) and its asymptotes.
The shaded region \(R\) is enclosed by the graph of \(y = \mathrm { f } ( x )\), the \(x\)-axis and the \(y\)-axis.
\includegraphics[max width=\textwidth, alt={}, center]{99b03f18-6dd6-437d-8b01-009ca7ab49ea-20_858_1002_1267_504}
16 - The shaded region \(R\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis to form a solid.
Find the volume of this solid.
Give your answer to three significant figures.
16
- (ii) The shaded region \(R\) is rotated through \(360 ^ { \circ }\) about the \(\boldsymbol { y }\)-axis to form a solid.
Find the volume of this solid.
Give your answer to three significant figures.
[0pt]
[4 marks]