Question: 1. (7 marks) Find - and d'y dx2 in each of the following cases. (a) y = sin vac (b) y2 - xy =10 (c)

1. (7 marks) Find - and d'y dx2 in each of the following cases. (a) y = sin vac (b) y2 - xy =10 (c) y = sin 2t, x = cos 2t for t c [0, 27] 2. (a) (2 marks) Differentiate the following functions. (i) y = 82x (ii) y = tanh(x2 + 1) (b) (3 marks) Evaluate the following integrals. (1) (2-2 - e' + 3sec' x)da V9 - 22 (ii) dx 3. (3 marks) Let a = (1, 4, 1), b = (1, -1, 4) and c = (1, 5, 1). Find the following. (a) The angle between a and b and the angle between b and c, noting any special relationships. (b) The component and projection of a on c. 4. (5 marks) Let L1 : + S. (a) Find the direction angles and direction cosines of the line L1. (b) Determine whether L1 and L2 are parallel, intersecting or skew. If the lines intersect, find the point of intersection. 5. (4 marks) Let the points P(2, 2, 0), Q(-1, 1, 1) and R(1, 4, 1) lie in the plane P. (a) Find a normal to the plane P. (b) Write down the vector parametric form and find the linear form of P

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