Question i. Show that ii. Solve the equation for , giving your answers correct to 3 significant figures. iii. Find Solution i. We are given; provided that provided that ii. We are required to solve the equation for . As demonstrated in (i); Therefore; […]
Question It is given that where a is a positive constant. i. Show that ii. Use the equation in part (i) to show by calculation that 1.5 < a < 1.6. iii. Use an iterative formula based on the equation in part (i) to find the value of a correct to 3 […]
Question A curve has equation Find the equation of the tangent to the curve at the point where it crosses the y-axis. Solution We are given that curve with equation and we are required to find the equation of the tangent to the curve at point where it crosses the y-axis i.e. . To […]
Question i. Solve the equation . ii. Hence solve the equation giving the value of u correct to 4 significant figures. Solution i. We are given the equation; Power Rule; Division Rule; and are inverse functions. The composite function is an identity function, with domain the positive real numbers. Therefore; Taking […]
Question i. Find the quotient when is divided by , and show that the remainder is 1. ii. Show that the equation has no real root. Solution i. Hence quotient is and remainder is . ii. We are required to show that following equation has no real roots; When […]
Question A curve has equation i. Find the x-coordinate of the stationary point. ii. Determine whether the stationary point is a maximum or minimum point. Solution i. First we are required to find the x-coordinate of the stationary point of the curve. A stationary point on the curve is the point where […]
Question Solve the inequality . Solution SOLVING INEQUALITY: PIECEWISE Let, . We can write it as; We have to consider both moduli separately and it leads to following cases; When If then above four intervals translate to following with their corresponding inequality; When When When If then above four intervals translate to following […]