A chemical reaction produces a foam whose volume $V$ (in $cm3\text{cm}^3$ ) changes at a rate $V^{'} (t)$ where $t\,$ is the time in seconds since the start of observation, for $t > 0$ .

Given that

$\dfrac{(t - 9)^2}{t\sqrt{t}}$
the observation point $P (4, 10)$ lies on the curve $V = g (t)$

(i) Find the value of the gradient of the curve at $P$ .

(ii) Hence find the equation of the tangent to the curve at $P$ , giving your answer in the form $a t + bV + c = 0$ , where $a$ , $b\,$ and $c\,$ are integers to be found.

Find $g (t)$ , simplifying your answer.

A chemical reaction produces a foam whose volume $V$ (in $cm3\text{cm}^3$ ) changes at a rate $V^{'} (t)$ where $t\,$ is the time in seconds since the start of observation, for $t > 0$ .

Given that

$\dfrac{(t - 9)^2}{t\sqrt{t}}$
the observation point $P (4, 10)$ lies on the curve $V = g (t)$

(i) Find the value of the gradient of the curve at $P$ .

(ii) Hence find the equation of the tangent to the curve at $P$ , giving your answer in the form $a t + bV + c = 0$ , where $a$ , $b\,$ and $c\,$ are integers to be found.

Find $g (t)$ , simplifying your answer.

1.11.2 Integrating standard functions

Question 92

Markscheme

1.11.2 Integrating standard functions

Question 92

Markscheme

1.11.2 Integrating standard functions

Question 92

1.11.2 Integrating standard functions Questions

1.11.2 Integrating standard functions

Question 92

1.11.2 Integrating standard functions Questions