Question The equation of a curve is y3+4xy=16 i. Show that . ii. Show that the curve has no stationary points. iii. Find the coordinates of the point on the curve where the tangent is parallel to the y-axis. Solution i. We are required to find . Hence; To find […]
Question i. Prove that . ii. Hence A. Solve the equation for . B. Find the exact value of Solution i. We are given that; provided that provided that ii. a. We are required to solve the equation; As demonstrated in (i); Hence; provided that Now we have […]
Question i. Given that show that the positive constant a satisfies the equation ii. Use an iterative formula, , with to find the value of 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 is: Rule for […]
Question The polynomials f(x) and g(x) are defined by; and where a and b are constants. It is given that (x + 2) is a factor of f(x). It is also given that, when g(x) is divided by (x + 1), the remainder is −18. i. Find the values of a and b. […]
Question The equation of a curve is Find the equation of the tangent to the curve at the point . Give the answer in the form y = mx + c, where the values of m and c are correct to 3 significant figures. Solution We are required to find the equation of tangent to […]
Question The variables x and y satisfy the equation where A and p are constants. The graph of against x is a straight line passing through the points (2,1.60) and (5, 2.92) as shown in the diagram. Find the values of A and p correct to 2 significant figures. Solution We are given; Taking natural […]
Question The polynomials f(x) and g(x) are defined by; and where a and b are constants. It is given that (x + 2) is a factor of f(x). It is also given that, when g(x) is divided by (x + 1), the remainder is −18. i. Find the values of a and b. […]
Question i. Solve the equation . ii. Hence, using logarithms, solve the equation , giving the answer correct to 3 significant figures. Solution i. SOLVING EQUATION: PIECEWISE Let, . We have to consider both moduli separately and it leads to following cases; OR We have the equation; We have […]