1. (4 Points) Mathematically prove that fxxy (x, y) = fyxx(x, y) for f(x,y)=x+xy'-2y (show all of your work). 2. (6 Points) (Multiple Choice). You must justify your answer either mathematically or in well written English sentences, whichever is most appropriate. a. (1 Point) The limit lim xexp(1x)-x i. Does not exist because co-cois not defined. ii. Converges to 1. iii. Is oo because xexp(x) grows faster than x. iv. Converges to 0. b. (1 Point) As gravel is being poured into a conical pile, its volume, V , changes with time. As a result, the height, h, and radius, r , also change with time. Knowing that at any moment V = ar h, the relationship between the changes with respect to time in the volume, radius, and height is: dV dt 1x 2r dr h+12 dh dt ii. dV 1 dt 37 2r dr . dh dt dt iii. dV = 1x 2rh+12 dh iv . dt = 3x (12) (1) + 2r.drin). c. (1 Point) If x=Sin (y) =arcsin(y), -T