Q1: Consider the piecewise defined function. Analyze the continuity of this function (4C)
Q2: Differentiate
a) b) (6K/U)
Q3: (4A)
Q4: An isosceles trapezoidal drainage gutter is to be made so that the angles at A and B in the
cross-section ABCD are each 120 degree. If the 5 m long sheet of metal that has to be bent to form the
open-topped gutter and the width of the sheet of metal is 60 cm, then determine the dimensions so that
the cross-sectional area will be a maximum.
(6T/I)
Q5: Determine f
11
(x).
a) f(x) = 4 sin
2
(x-2) b) f(x) = 2(cos x) (sec
2 x) (6K/U)
Q6: If y = e
2x – 1, prove that dy = 1-y
2
.
———– —– (5A)
e
2x +1 dx
(3T/I)

12. Find the points on the graph of y = 1 x
    3 – 5x – 4 at which the tangent is horizontal. (3K/U)

3 x

13. Determine the slope of the tangent to h(x) = 2x(x + 1)
    3
    (x
    2 + 2x + 1)
    2 at x = -2.Explain how to find the
    equation of the normal at x = -2.