The curve $C\,$ has equation

\frac{18}{4(2x - k)}, \quad x \not= \frac{k}{2}

where $k\,$ is a positive constant and $\neq 2$ .

Find $dydx\displaystyle \frac{dy}{dx}$ giving your answer in simplest form in terms of $k$ .

The point $P\,$ with $x\,$ coordinate 1 lies on $C$ . Given that the gradient of the curve at $P\,$ is -9, find the two possible values of $k$ .

Given also that $k < 2$ , find the equation of the normal to $C\,$ at $P$ , writing your answer in the form $a x + b y + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

Show, using algebraic integration, that

\int_{1}^{3} \frac{18}{4(2x - k)} \, dx = \lambda \ln(5)

where $\lambda\,$ is a constant to be found.

The curve $C\,$ has equation

\frac{18}{4(2x - k)}, \quad x \not= \frac{k}{2}

where $k\,$ is a positive constant and $\neq 2$ .

Find $dydx\displaystyle \frac{dy}{dx}$ giving your answer in simplest form in terms of $k$ .

The point $P\,$ with $x\,$ coordinate 1 lies on $C$ . Given that the gradient of the curve at $P\,$ is -9, find the two possible values of $k$ .

Given also that $k < 2$ , find the equation of the normal to $C\,$ at $P$ , writing your answer in the form $a x + b y + c = 0$ , where $b\,$ and $c\,$ are integers to be found.

Show, using algebraic integration, that

\int_{1}^{3} \frac{18}{4(2x - k)} \, dx = \lambda \ln(5)

where $\lambda\,$ is a constant to be found.

1.11.2 Integrating standard functions

Question 87

Markscheme

1.11.2 Integrating standard functions

Question 87

Markscheme

1.11.2 Integrating standard functions

Question 87

1.11.2 Integrating standard functions Questions

1.11.2 Integrating standard functions

Question 87

1.11.2 Integrating standard functions Questions