Question A curve is such that and (1, 4) is a point on the curve. i. Find the equation of the curve. ii. A line with gradient is a normal to the curve. Find the equation of this normal, giving your answer in the form . iii. Find the area of the region enclosed by the curve, the […]
Question The equation of a curve is and the equation of a line is , where is a constant. i. In the case where , find the coordinates of the points of intersection of and the curve. ii. Find the set of values of for which does not intersect the curve. iii. In the case where , one of the […]
Question The diagram shows the cross-section of a hollow cone and a circular cylinder. The cone has radius 6 cm and height 12 cm, and the cylinder has radius cm and height cm. The cylinder just fits inside the cone with all of its upper edge touching the surface of the cone. i. Express h in terms of r and […]
Question The equation of a curve is . i. Show that the whole of the curve lies above the x-axis. ii. Find the set of values of x for which is a decreasing function of x. The equation of a line is , where k is a constant. iii. In the case where k = 6, find the coordinates of the […]
Question A curve has equation . i. The normal to the curve at the point (4, 2) meets the x-axis at P and the y-axis at Q. Find the length of PQ, correct to 3 significant figures. ii. Find the area of the region enclosed by the curve, the x-axis and the lines x = 1 and […]
Question Find the gradient of the curve at the point where x = 3. Solution Gradient (slope) of the curve is the derivative of equation of the curve. Hence gradient of curve with respect to is: In the given case: We can rewrite the equation as; Rule for differentiation of is: Rule for differentiation of is: Rule for differentiation of […]