I. TRUE or FALSE. Write TRUE if the statement is always true, otherwise write FALSE. [14pts] 1. If z = f (x, y), then the first partial derivative of z with respect to y is given by Zy = lim f ( x+Ax,y+Ay)-f(x,y) Ay-0 Ay 2. If f (x, y) = vxy, then az f axdy 4vxy 3. If f ( x, y) = e-xy4+x2 2x+3y then its first partial derivative with respect to y is 4y-7x 2y3e-x (1 4 + x2) 2+ 29x (4y-7x)2 4. Geometrically, the partial derivative of a function z = f(x, y) with respect to one of its variables is the slope of the curve given by the intersection of z and a plane in either the x or y direction. 5. Suppose z = f(x,y) = x2e-6y + sin(x6 - 4x + 1), then Zyxxy = 72e-by. 6. The differential dz = [y?sec2(xy?)]dx + [2xy sec2(xy?)]dy is the total differential of the given function z = f(x, y) = tan(xy2). 7. If f (x, y) =, then fx (2, -1) = 1