Question The sequence of values given by the iterative formula With initial value , converges to . i. Determine the value of correct to 3 decimal places, giving the result of each iteration to 5 decimal places. ii. State an equation satisfied by and hence find the exact value of . Solution […]
Question The sequence of values given by the iterative formula With initial value , converges to . i. Determine the value of correct to 3 decimal places, giving the result of each iteration to 5 decimal places. ii. State an equation satisfied by and hence find the exact value of . Solution […]
Question The diagram shows the curve and its stationary point M. The x-coordinate of M is m. i. Find an expression for and hence show that . ii. Use an iterative formula based on the equation in part (i) to find the value of m correct to 4 significant figures. Give the result […]
Question i. It is given that the positive constant a is such that ii. Show that iii. Use an iterative formula , to find a correct to 3 decimal places. Give the result of each iteration to 5 decimal places. Solution i. We are given that; Rule for integration of […]
Question The equation of a curve is . At the point on the curve with x-coordinate p, the gradient of the curve is . i. Show that . ii. Show by calculation that 3.3 < p < 3.5. iii. Use an iterative formula based on the equation in part (i) […]
Question The equation of a curve is . At the point on the curve with x-coordinate p, the gradient of the curve is . i. Show that . ii. Show by calculation that 3.3 < p < 3.5. iii. Use an iterative formula based on the equation in part (i) […]
Question The equation of a curve is . At the point on the curve with positive x-coordinate p, the gradient of the curve is . i. Show that . ii. Show by calculation that 2 < p < 3. iii. Use an iterative formula based on the equation in part […]