6. Use a two path test to show that the limits do not exist x2 -y a) lim (x,y)-(0,0) x-y b) lim xy - y (x,y)-(1,0) (x-1)2+y27. z = In(e* +e") Determine whether the following statements are true or false. Show all the details of your work. a) zo az ax dy b) - ax 2 dy ? axdy =0 8. Verify that Wxy = Wyx w = xy2 + x2y3 + x3 y4\f11. Assume thatz = f(x,y),x = g(t),y = h(t),c(2, 1) = 3, and fy(2,1) = 2. If 9(0) = 2.h(0) = -1.g'(0) = 5, and h'(0) = 4, find Eat it = 0. 12. Consider the function and the point P0 x. )3 Z) = 1n xy + 1n yz + 1n xz, P0(1, 1, 1) a) Find the directional derivative for the function fat the point P0 in the direction of the vector m where Q0(2,3,4). b) Find the directions in which the function increases and decreases most rapidly at P0. c) Find the derivatives of the function in these directions