1. (10p) Find an equation for the plane that passes through the line of intersection of the planes r + 2y+ z =5 and x- y +2z =1, and is perpendicular to the plane 3x + 2y - 2z = 1. 2. (10p) Parametrization y = In(x2) and find its curvature. 3. (10p) Find the following limit if it exists, or prove that it does not exist: lim y(ex - 1) (z,y)-(0,0) 32 + 14 4. (10p) Find and classify the critical points of f(x, y) = 5x2y + 2y3 - 10x2 - 3y2 + 1. 5. (10p) A rectangular box without a lid is to be made from 12 m' of cardboard. Find the maximum volume of such a box. 6. (10p) Evaluate y 1472dA where D is the region bounded by y = VI, y = 0, and r = 1. 7. (10p) Use spherical coordinates to evaluate y2 /4-12- y' vx2 + y2 + 22 dadx dy. 4-12- 8. (10p) Show that the vector field F(x, y, 2) = is conservative. 9. (20p) Verify Green's theorem for the vector field F(x, y, 2) = > and the triangle with vertices (0, 0), (1, 0), (0, 1)