Question i. Prove the identity ii. Hence solve the equation For . Solution i. We are given that; We utilize following two addition formulae; ii. We are required to solve; As demonstrated in (i); Therefore; Since provided that ; Since ; Therefore, we solve for . […]
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 1.3 and 1.4. iii. Show that, if a sequence of values given by the iterative formula converges, then it converges to the […]
Question The equation of a curve y=x3e-x. i. Show that the curve has a stationary point where x = 3. ii. Find the equation of the tangent to the curve at the point where x = 1. Solution i. We are required to show that the curve has […]
Question a. Show that b. By using an appropriate trigonometrical identity, find the exact value of Solution a. We are required to show that; Rule for integration of is: b. We are required to find exact value of; We know that , therefore; Hence; Rule for integration of is: Rule for integration […]
Question The diagram shows the part of the curve y = xe-x. The shaded region R is bounded by the curve and by the lines x = 2, x = 3 and y = 0. i. Use the trapezium rule with two intervals to estimate the area of R, giving your […]
Question The polynomial , where a and b are constants, is denoted by . It is given that when is divided by the remainder is 30, and that when is divided by the remainder is 18. i. Find the values of and . ii. When a and b have these values, […]
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 with […]
Question Given that 13x = (2.8)y, use logarithms to show that y = kx and find the value of k correct to 3 significant figures. Solution We are given; Taking natural logarithm of both sides; Power Rule;