In these problems you should show all of your work in eomplete mathematical \"sentences\". writing eompletc English sontenees when you explain your logic. Please always staple your homewrirk and label it with your section number. Late homework will not be accepted. 1. Suppose f is a differentiable functions of a: and y= and g(r', 3) = f(2r' s, s2 41'). Use the table of values to calculate 9,41, 2) and 99(1, 2). 2. If a = f{.-r:, y). where .1: = e\" cost autl y = c" slut, show that 02'\". + 021:. ('qu 021:. + 02-\". (33:2 a\"! _ as? as ' 3. (a) if u = (a, b) is a unit vector and f has continuous second partial derivatives, show that Dif : furl?! 'i' 230$be 'i' fyybz 23\" in the direction of v = (4, 6). (b) Find the second directional derivative of f(:::, y) = we 4. Show that every normal line to a sphere passes through the center of the sphere. .1. Show that f(.-:r,;:,r) = 3:2 + 43/2 4mg; + 2 has an infinite number of critical points and D = (l at. each one Then show that f has a local (and absolute) minimum at each critical point. 6. Find the absolute maximum and minimuln values of f(;e, y) = 3 + my :r: 21:; over the closed triangular region with vertices {1, U), 5, (l), and (1,4). 7. Find the points on the surface y2 = 9 + 3:2: that are closest to the origin. 8. Use Lagrange multipliers to nd the maxil'nuni and minimum values of ag-1;, z) = 1174 + 394 + 2:'1 subject to the constraint 3:2 + y? + zr'Z = 1. 9. Use the method of Lagrange multipliers to solve Question 7