School of MAE, MA2006 CA2 Open Book 1. The air pressure in a particular room varies from point to point and is given by T(x, y,z) = xz+5xyz' -e", where (x. y, =) describes a general point in the room (with reference to a Cartesian coordinate system). (a) At the point (1, 4, 1), calculate the rate of change of pressure per unit distance along the direction J. of the vector, -37 + 2j (b) At the point (1, 4, 1), find all the directions along which the rate of change of pressure per unit distance is zero. Assume those directions are in the form of ar + by + ck . Your solution only needs to give a relation among a, b and c. (c) At the point (1, 4. 1), find the direction (give your solution in unit magnitude vector) along which the rate of increase in the pressure per unit distance is the greatest. What is the greatest rate of increase in the pressure per unit distance at the point (1, 4. D)? For Q1, if you like (but not necessary), you can give your answers in numerical digits with 2 decimal places. (50 marks) 2. Let S be the portion of the surface x- -2x + j' + - -8 for 1 25 2 2. Find the area of the surface S. Surface integral formula: /4. for the surface given by = = /(1 1) (50 marks )