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9709 P31 - Jun 2014 - Q10
1691

The diagram shows the curve \(y = 10e^{-\frac{1}{2}x} \sin 4x\) for \(x \geq 0\). The stationary points are labelled \(T_1, T_2, T_3, \ldots\) as shown.

(i) Find the \(x\)-coordinates of \(T_1\) and \(T_2\), giving each \(x\)-coordinate correct to 3 decimal places.

(ii) It is given that the \(x\)-coordinate of \(T_n\) is greater than 25. Find the least possible value of \(n\).

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