Question The equation of a curve is i. Find an expression for and show that the gradient of the curve at the point (−1, 2) is . ii. Show that the curve has no stationary points. iii. Find the x-coordinate of each of the points on the curve at which the […]
Question a. Showing all necessary working, solve the equation for . b. Showing all necessary working, solve the equation for . Solution a. We are given; provided that provided that Let , then; We are given that ; interval for can be found as follows. Multiplying entire inequality with 2; Hence, […]
Question It is given that Where is a constant. i. Show that ii. Using the equation in part (i), show by calculation that 0.5 < a < 0.75. iii. Use an iterative formula, based on the equation in part (i), to find the value of a correct to 3 significant figures. Give […]
Question The polynomial is defined by where is a constant. It is given that is a factor of i. Find the value of a . ii. Using this value of a, factorise completely. iii. Hence solve the equation , giving the answer correct to 2 significant figures. Solution i. We are […]
Question A curve has equation Find the exact gradient of the curve at the point for which y = 4. Solution We are required to find the gradient of the curve at a point where y=4. Gradient (slope) of the curve at the particular point is the derivative of equation of the curve at that […]
Question Find the exact value of Solution We are given that; Rule for integration of is: Rule for integration of , or ; Rule for integration of is:
Question i. Solve the inequality . ii. Hence find the largest integer n satisfying the inequality . Solution SOLVING INEQUALITY: PIECEWISE i. 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 […]