1.3 Functions

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Question 98

A mechanical system's power output $G (t)$ at time $t$ is modeled for $t > 3$ by the function

\frac{t^4 - t^3 - 4t^2 + 3t - 2}{t^2 - t - 6}

Given that

\equiv t^2 + A + \frac{B}{t - 3}

find the value of the constant $A$ and show that $B = 5$ .

[4]

The curve $K$ has equation $y = G (t)$ for $t > 3$ .

Find the equation of the tangent to $K$ at the point where $t = 4$ . Give your answer in the form $y = m t + c$ , where $m$ and $c$ are constants to be found.

[4]

The region $S$ is bounded by the curve $K$ , the $t$ -axis, and the vertical lines with equations $t = 4$ and $t = 5$ . Find the exact area of $S$ , writing your answer in the form $\ln 2$ , where $a$ and $b$ are constants to be found.

[5]

1.3 Functions

Question 98

A mechanical system's power output $G (t)$ at time $t$ is modeled for $t > 3$ by the function

\frac{t^4 - t^3 - 4t^2 + 3t - 2}{t^2 - t - 6}

Given that

\equiv t^2 + A + \frac{B}{t - 3}

find the value of the constant $A$ and show that $B = 5$ .

[4]

The curve $K$ has equation $y = G (t)$ for $t > 3$ .

Find the equation of the tangent to $K$ at the point where $t = 4$ . Give your answer in the form $y = m t + c$ , where $m$ and $c$ are constants to be found.

[4]

[5]

1.3 Functions

Question 98

Markscheme

1.3 Functions

Question 98

Markscheme

1.3 Functions

Question 98

1.3 Functions Questions

1.3 Functions

Question 98

1.3 Functions Questions