The temperature $H$ (in $∘C^{\circ}\text{C}$ ) of a specialized thermal probe is modeled as a function of time $t$ (in seconds, $t > 0$ ), where $H = g (t)$ .

It is known that:

At $t = 9$ , the temperature of the probe is $15∘C15^{\circ}\text{C}$ .
The rate of change of temperature is given by $\dfrac{45}{t^2} + \dfrac{3}{2\sqrt{t}} - 2$

Determine the equation of the tangent to the curve $H = g (t)$ at the point where $t = 9$ . Give your answer in the form $H = m t + c$ , where $m\,$ and $c\,$ are constants.

Find an expression for $g (t)$ in its simplest form.

The temperature $H$ (in $∘C^{\circ}\text{C}$ ) of a specialized thermal probe is modeled as a function of time $t$ (in seconds, $t > 0$ ), where $H = g (t)$ .

It is known that:

At $t = 9$ , the temperature of the probe is $15∘C15^{\circ}\text{C}$ .
The rate of change of temperature is given by $\dfrac{45}{t^2} + \dfrac{3}{2\sqrt{t}} - 2$

Determine the equation of the tangent to the curve $H = g (t)$ at the point where $t = 9$ . Give your answer in the form $H = m t + c$ , where $m\,$ and $c\,$ are constants.

Find an expression for $g (t)$ in its simplest form.

1.11.2 Integrating standard functions

Question 83

Markscheme

1.11.2 Integrating standard functions

Question 83

Markscheme

1.11.2 Integrating standard functions

Question 83

1.11.2 Integrating standard functions Questions

1.11.2 Integrating standard functions

Question 83

1.11.2 Integrating standard functions Questions