The curve with equation y = e^2x ln(x – 1) has a stationary point when x = p. (i) Show that p satisfies the equation x = 1 + exp exp(2(x-1)) where exp(x) denotes ex. (ii) Verify by calculation that p lies between 2.2 and 2.6. (iii) Use an iterative formula based on the equation in part (i) to determine p correct to 2 decimal places. Give the result of each iteration to 4 decimal places.

The sequence of values given by the iterative formula x_n+1 = (2x_n^6 + 12x_n) / (3x_n^5 + 8) with initial value x₁ =...

A curve has equation y = x³e⁻⁰.²ˣ where x ≥ 0. At the point P on the curve, the gradient of the curve is 15.

Two planes have equations 2x + 3y – z = 1 and x – 2y + z = 3.

The diagram shows the curve y = sin³x √(cos x) for 0 ≤ x ≤ ½π, and its maximum point M. [Figure 10.1]

A small ring P of mass 0.03 kg is threaded on a rough vertical rod. A light inextensible string is attached to the ri...