Question i. Express in the form , where and , giving the exact values of R and . ii. Hence show that iii. By differentiating , show that if then . iv. Using the results of parts (ii) and (iii), show that Solution i. We […]
Question The diagram shows the curve y = 2ex + 3e-2x. The curve cuts the y-axis at A. i. Write down the coordinates of A. ii. Find the equation of the tangent to the curve at A, and state the coordinates of the point where this tangent meets the x-axis. […]
Question i.By expanding , show that ii.Hence, or otherwise, show that Solution i. We have; We apply following addition formula. Therefore; We apply following two formulae. We have the trigonometric identity; Therefore, we can replace; Hence; ii. We are required to show that; As we have demonstrated in […]
Question A curve has equation . i. Write down expressions for and ii. Find the coordinates of the stationary point on the curve and determine its nature. iii. Find the volume of the solid formed when the region enclosed by the curve, the x-axis and the lines x = 1 and x = 2 is rotated […]
Question A curve is such that and is a point on the curve. i. Find the equation of the normal to the curve at P, giving your answer in the form . ii. Find the equation of the curve. Solution i. To find the equation of the normal to the curve at P; To find the equation […]
Question The diagram shows part of the graph of and the normal to the curve at . This normal meets the -axis at R. The point Q on the -axis and the point S on the curve are such that PQ and SR are parallel to the -axis. i. Find the equation of the normal at P […]
Question Evaluate Solution Writing the given expression in standard form; Rule for integration of is: In the given case;