F. Sketch the region onto which the sector r ≤ 1,0 ≤ 0 ≤/4 is mapped by the transfor- mation (a) w = z²; (b) w = z³; (c) w = z².

1S Let R be the region in the xy plane bounded by the curres y=X-8x and y=-6x+3. Set ye, but do not evaluatejanintegral that calculates CA)of n. AS rCx²-8xJ- (-6x t3) the area dx Ta-をx)-Coxts)da 3. GLS -8- 3J -8 コ 2. 2.

S is the region bounded by paraboloid z=9-x^2-y^2 and the xy plane

Let S be the surface which is the graph of a C¹ function f(x, y) defined on an elementary region D. Then the area A(S) of S is given by 01/₂√₁+ 11 6₁ 1 + (f(x, y))² dxdy f(x, y) dxdy 2 √¹ - ² () - (or) af 1² dx ду D 2 °1/₂ √√₁ + ( 2 ) + ( )* dxd's af dy D f f 01/√√1+#+ / dx² дуг D xảy dxdy