1. Consider the following function f(x, y) = 2x32 + -. [7) (a) Find the linearization L(x, y) to f(x, y) at the point (2, 1). [3) (b) Use this linearization to estimate the value of f (1.9, 2.3). [12] 2. Suppose u = u(x, y) and v = v(x, y) are differentiable and satisfy du av Ou av ay - and ay ax If x = rcos0 and y = r sin 0, prove that 1 adv av 1 du ar and r 20 [12] 3. Find the volume of the solid under the surface z = x2 + y? + 1 and above the region R bounded by y = x2 and y - 2x - 3 = 0 on the xy-plane. 4. For the following integrals: (i) Sketch the region of integration, (ii) Reverse the order of integration. (you do not have to evaluate the integrals). 141 (2 ) In(zy) du dy 14 () 1. pln(x) sin(x - y) dy dx