Need help with multivariable calculus

02 a} Show that x, y) = x achieves a minimum value on the closed curve C defined by x4 x3+ y2 = 0. Identify what theorem you are using. b} Use Lagrange multipliers to find this minimum value and where it occurs. 03 Consider TtxJ) = (xy, x2 )3). a) Show that T has an inverse with continuous partial derivatives at the point (1, i). b) Calculate the linear approximation to T'1 at (.11, i). c} Where is the Jacobian determinant of this mapping 0? Is the function onetoone in a neighbourhood of this point? 04 Consider a convex function f : IR > [R and a convex function g : [R2 > [R . Show that if for all u. v E IR , u s v implies f(u) 5 y) then fa g is a convex function. 05 Calculate the volume V of the region bounded by z = 1'/x2+ F, x2+ )2: 9 , z = 0. 06 Let V be the volume cut out of x2+ y2 = 1 by the planes z = 2y, z = y where y z 0 . Set up iterated integrals equal to V in the form " dxdy and also 1?" dydx. Evaluate the integral using either order