A curved profile for a glass sculpture $C\,$ is modeled by the parametric equations

\frac{1}{4}t^2 + 1, \quad y = 2t - \frac{8}{t}, \quad t > 0

The curve $C\,$ intersects the $x$ -axis at the point $Q$ .

Find the $x$ -coordinate of $Q$ .

The line $l\,$ is the normal to $C\,$ at the point $P$ . Given that $t = 4$ at $P$ :

Write down the coordinates of $P$ .

Using calculus, show that an equation of $l\,$ is

4 x + 5 y = 50

The region $R\,$ is bounded by the curve $C$ , the line $l$ , and the $x$ -axis.

Using algebraic integration, find the exact volume of the solid of revolution formed when the region $R\,$ is rotated through $2\pi\,$ radians about the $x$ -axis.

A curved profile for a glass sculpture $C\,$ is modeled by the parametric equations

\frac{1}{4}t^2 + 1, \quad y = 2t - \frac{8}{t}, \quad t > 0

The curve $C\,$ intersects the $x$ -axis at the point $Q$ .

Find the $x$ -coordinate of $Q$ .

The line $l\,$ is the normal to $C\,$ at the point $P$ . Given that $t = 4$ at $P$ :

Write down the coordinates of $P$ .

Using calculus, show that an equation of $l\,$ is

4 x + 5 y = 50

The region $R\,$ is bounded by the curve $C$ , the line $l$ , and the $x$ -axis.

Using algebraic integration, find the exact volume of the solid of revolution formed when the region $R\,$ is rotated through $2\pi\,$ radians about the $x$ -axis.

Differentiation

Question 98

Markscheme

Differentiation

Question 98

Markscheme

Differentiation

Question 98

Differentiation Questions

Differentiation

Question 98

Differentiation Questions