1. Use the chain rule to find . and ay "' for y'cos (5z - 2x) = 1 + esin(6zy). 2. Find the directional derivative of the function f(x, y, 2) = xtan-'(y/2) at the point (2, 1, 1) in the direction of the vector v = (1, 1, 1). 3. Use differentials to approximate the value of 8.94\/9.99 - (1.01)3. 4. The dimensions of a closed rectangular box are measured as 80 cm, 60 cm and 50 cm respectively, with a possible error of 0.2 in each dimension. Use differentials to calculate the maximum error in calculating the surface area of the box. 5. Find the gradient of the function g(x, y) = Invx2 + y2 at (1, 2). 6. Find equations of the tangent plane and the normal line to the surface re = = 1 at the point (1, 0, 5). 7. Suppose you are climbing a hill whose shape is given by the equation z = f(x, y) = 1000-0.01x2-0.02y', where r, y, and z are measured in meters, and you are standing at a point P(60, 100, 764). (a) In which direction should you proceed initially in order to reach the top of the hill fastest? (b) What is the maximum rate of ascent at P? 8. Find the local maximum and minimum values and saddle points of the function. (i) f(x,y) = 3xy - aly - ry?. (ii) g(x, y) = y' - 2y cost, -1