Q1 a) Find for y = x3/2In3x (note in is natural log, i.e. log.) [4 marks] b) Find " for y = 3tan*3x [4 marks] c) Determine J x* Inx dx [4 marks] d) Determine fxv2x2 + 1dx [4 marks] e) Calculate the angle between vectors a = (o ) and b - (2) [4 marks] f) 10 litres of a solution contains 15% pollutant. How much water needs to be added to dilute it to a solution with 0.5% pollutant? [4 marks] g) A constant speed boat takes 3 hours to travel 40km going against the constant flow of a river, but takes only 1.5hrs for the return journey going with the river flow. What are the speeds of the boat and river flow? [4 marks] h) Find the determinant det(X) of the matrix X = [4 marks] i) Find for z = cosxsiny [4 marks] j) Find lim 1-cosx [4 marks] X-0