The diagram shows part of the curve with parametric equations x = 2 In(t + 2), y

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The diagram shows part of the curve with parametric equations

x = 2 In(t + 2), y = t+ 2t + 3.

i. Find the gradient of the curve at the origin.

ii. At the point P on the curve, the value of the parameter is p. It is given that the gradient of the curve at P is 1/2.

a. Show that P = 1/3p2 + 2 -2.

b. By first using an iterative formula based on the equation in part a, determine the coordinates of the point P. Give the result of each iteration to 5 decimal places and each coordinate of P correct to 2 decimal places.

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