2. a) Find the general integral of the equation zwa+ywy = ryw in the domain {(x,y): >0, y>0}. b) Find the solution of this equation in the domain {(x, y): z>0, y>0} such that w(x, 1) = 1.

Exercise 1- Determine which of the following functions are analytic: 2 2 d- x²+iy², b = 2xy + i(x²y²) 1 d= (2-1)(2+1) x-iy x²+y2 E- Sinx coshy+icosx sinhy C- )

Find the mass M of a fluid with a constant mass density flowing across the paraboloid z = 36 - x² - y², z ≥ 0, in a unit of time in the direction of the outer unit normal if the velocity of the fluid at any point on the paraboloid is F = F(x, y, z) = xi + yj + 13k. (Express numbers in exact form. Use symbolic notation and fractions where needed.) M = Incorrect 31740πσ > Feedback Use A Surface Integral Expressed as a Double Integral Theorem. Let S be a surface defined on a closed bounded region R with a smooth parametrization r(r, 0) = x(r, 0) i + y(r, 0) j + z(r, 0) k. Also, suppose that F is continuous on a solid containing the surface S. Then, the surface integral of F over S is given by [[F(x, y, z) ds = = D₁² Recall that the mass of fluid flowing across the surface S in a unit of time in the direction of the unit normal n is the flux of the velocity of the fluid F across S. M = F(x(r, 0), y(r, 0), z(r, 0))||1r × 1e|| dr de F.ndS X

4. a) Find the differential of the function f (x, y) = e*y at the point (2, 0) %3D b) Find the tangent plane approximation for the value f(1.9, -0.1) for the function in part a)