14 The graph of \(y = \frac { 2 x ^ { 3 } } { x ^ { 2 } + 1 }\) is shown for \(0 \leq x \leq 4\)
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Caroline is attempting to approximate the shaded area, \(A\), under the curve using the trapezium rule by splitting the area into \(n\) trapezia.
14
- When \(n = 4\)
14 - State the number of ordinates that Caroline uses.
14
- (ii) Calculate the area that Caroline should obtain using this method.
Give your answer correct to two decimal places.
14 - Show that the exact area of \(A\) is
$$16 - \ln 17$$
Fully justify your answer.
| 14 | Explain what would happen to Caroline's answer to part (a)(ii) as \(n \rightarrow \infty\) | [1 mark] | Do not write outside the box |
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