Convert the double integral [[ (x + y)ex²-y² dA to uv-plane where R is the rectangle enclosed by the lines x - y = 0, x − y = 2, x + y = 0 and x + y = 3, using the change of variables x = -— (u + v). y = -— (u – v).

: Find the derivative of f(x, y, z) = x³ - xy² - z at the point po (2,1,0) in the direction of vector v = 2i - 3j + 6k.

Use the polar form of C-R equations to verify that C-R conditions hold in case of f:C +C where f(2) = z12, (z e C). Then verify that f'(a) = 12a" for all points а.