Use the Divergence Theorem to evaluate SfF.N F. N ds and find the outward flux of F through the surface of the solid S bounded by the graphs of the equations. Use a computer algebra system to verify your results. F(x, y, z) = (xy² + cos z)i + (x²y + sin z)j + e²k = 1/² √√x² + y²₁ ,Z = 4 S: z =

Use stokes theorem to solve number 4.

Consider the function f : R² → R² defined by f(x, y) = (xeª cos y — yeª sin y, eª y cos y + xeª sin y). It is given that the corresponding complex function f : C → C is holomorphic on its domain. (a) State the Cauchy-Riemann equations. You do not have to show that they hold for f.

y=t√y (0) Determine if the has erential equation a unique solis