Sketch the graph of $y=\frac{1}{{{\left( x-2 \right)}^{2}}}-1$ , showing clearly all asymptotes.[2

Question

Sketch the graph of $y=\frac{1}{{{\left( x-2 \right)}^{2}}}-1$ , showing clearly all asymptotes.[2] The region $R$ is bounded by $x-$axis and the curve from $x=0$ to $x=\frac{3}{2}$. Find the exact value of the area of $R$.[3] The region $R$ is rotated $2\pi $ radians about the $y$-axis. Find the volume of the solid generated, giving your answer correct to $3$ decimal places.[4]

Accepted Answer

(i) $1\text{ unit}^2$ (ii) $\dfrac{7\pi}{4}\text{ units}^3\approx5.498\text{ units}^3$

2006 HCI Promo Q13

2006 HCI Promo Q13

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