There are six questions in this assignment.  Answer all questions. You may use illustrations and diagrams to enhance your explanations.  

1. Differentiate y w.r.t. x where
                           (3 marks)

2. Find:  (1 ½ marks)
3. If f(x) =
   
   
   Find whether f is continuous at x = 9.  (2 ½  marks)
   
4. For the following function, find a point of maxima and a point of minima, if these exist f(x) = 12x6 – 4x4 + 15x3 –1. (3 marks)

5. If α, b, g are the roots of the equation 3x3 5x2 + 2x + 5 = 0 Find the equation whose roots are α2 + b2 + bα , b2 + g2 + g b,   g2 + α2 + gα     (5 marks)

6. Evaluate:      (2 marks)
7. Find all the seventh roots of (3+4i).   (1 marks)
8. Find the area bounded by the x-axis, the curve y = e2x and the ordinates x = 4 and x = 7. (3 marks)
9. (a): Find the equation of the line joining the points (-7, 6,-3) and (7, -6, 3).  (1 marks)
   (b) Find the equation of the sphere, which contains the circle x² + y² + z² = 18  , 3x + 3y + 3z = 11  and passes through the origin.   (3 marks)