Question The parametric equations of a curve are for . At the point P on the curve, the gradient of the curve is 2. i. Show that the value of the parameter at P satisfies the equation . ii. By first expressing in the form , where R > 0 and , find […]
Question a. Show that b. Find Solution a. We are required to show; Rule for integration of is: Rule for integration of is: Division Rule; Power Rule; Multiplication Rule; b. We are required to find; provided that provided that Rule for integration of is: Rule for integration of is: Rule for […]
Question The curve with equation and the point P on the curve has y-coordinate 10. i. Show that the x-coordinate of P satisfies the equation ii. Use the iterative formula to find the x-coordinate of P correct to 4 significant figures. Give the result of each iteration to 6 significant figures. iii. Find the gradient […]
Question The variables x and y satisfy the equation y = Aepx+p, where A and p are constants. The graph of ln y against x is a straight line passing through the points (1, 2.835) and (6, 6.585), as shown in the diagram. Find the values of A and p. Solution We are given; Taking […]
Question Given that satisfies the equation find the value of Solution SOLVING EQUALITION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have to consider both moduli separately and it leads to following cases; This cannot be solved. Hence, the solution for […]
Question i. Show the equation For . Show all necessary working. Solution We are given that; Let , then; Now we have two options. Since ; Using calculator Now we find all solutions in the interval . Properties of Domain Range Periodicity Odd/Even Translation/ Symmetry We utilize the periodicity/symmetry property of to find […]