Show all work to receive any credit. Correct answers without supporting work will receive NO credit! 1. Sketch in the ry - plane the domain of each function : (a) f(x,y) = (Vx-1+ vy +1) . In(x2 + y? -4) e-ry (b) g (1, y) = 2x + 5y (c) h(x,y) = sin (x) + tan-1 (y). 2. Explain why there is not a level curve for f (x, y) = + smy) for k = =1. 12 + yz 3. Graph three level curves for the function f (r, y) = = It by selecting three values of I - y k of your own choice in the range of f. 4. Use polar coordinates to find each limit : (a) lim (x.y)-+(0.0) 2 + y2 (b) lim (x' + y ) In (x2 + y?). (F.y)-+(0,0) 5. Explain why the path y = r+1 cannot be used to evaluate the limit lim (2.0)-+(2.0) VI - 2+ y Do not evaluate the limit. Just explain why you cannot use y = r + 1 as a path . 6. Find each limit or show that the limit does not exist: (a) lim 2.12 12 - 2 (x,y)-(1.1) 2:2 + 12 - 2 (b) ry + 1 lim (x.y)-+(0.0) 23 + 12 + 1 (c) lim (x.y)-(0.0) /2+ 72+ 1-1 7. If lim f (x, y) = 2022, is it possible for f (1, 2) = 3033 ? Fully explain to receive (x.) -(1.2) full credit