Hits: 115
Hits: 115 Question i. Prove the identity ii. Hence solve the equation For . Solution i. We are required to prove the identity; We know that; Therefore; provided that ii. We are required to solve the equation; From (i) we know that; Therefore; Since , therefore Let […]
Hits: 84 Question A. Find the exact area of the region bounded by the curve , the x-axis and the lines and . The diagram shows the curve , for and its minimum point M. Find the exact x- coordinate of M. Solution A. We are required to find area under the […]
Hits: 92 Question i. By sketching a suitable pair of graphs, show that the equation has only one root. ii. Verify by calculation that this root lies between x = 0.7 and x = 0.8. iii. Show that this root also satisfies the equation iv. Use the iterative […]
Hits: 80 Question The equation of a curve is x2− 2 x2y+ 3y = 9. i. Show that ii. Find the equation of the normal to the curve at the point where x = 2, giving your answer in the form ax + by + c = 0. Solution i. […]
Hits: 47 Question A curve is such that . The point (3, 2) lies on the curve. Find the equation of the curve. Solution We can find equation of the curve from its derivative through integration; For the given case; Therefore; Rule for integration of is: This integral is valid only when . If a […]
Hits: 205 Question The variables x and y satisfy the relation . i. By taking logarithms, show that the graph of y against x is a straight line. ii. Find the exact value of the gradient of this line and state the coordinates of the point at which the line […]
Hits: 213 Question i. The polynomial , where is a constant, is denoted by . It is given that is a factor of . Find the value of . ii. When has this value, find the remainder when is divided by . Solution i. We are given that; We […]
Hits: 108 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 […]