Find the total flux of the vector field F= (x^2 z)i + (y^2 z)j+(z^3)k through the closed surface of the cylinder given by x^2 + y^2= 16 ,  z=2,   z=−2

Use the substitution u=-3x+2y to solvethe differential equation (-3x+2y) y'= - 1. a) Clearly classify the equation obtained after the substitution b) on the plane (x, u) sketch at least three vectors of the slope field with different slopes Attach File

1) F=Cy+2xz)i+ (x+ z²+1)j +(2yz+x)K Give the Vector field. Protected, ☆Fis the vector fied protected! Your show. If find a Potential function for the vector field "F".

Find a scalar field, 0, whose gradient is the irrotational vector V = (x² - yz, y² — xz, ² - xy) In other words, find such that Vo=V₁ Note: • Remember that your tutorial has Hints in it, at the end of each chapter. If you're stuck, they are often quite useful! • If the answer is a scalar, you can just type it in the box (using the Calcpad if you like, or using / for fractions, ^ for exponents, shift and - for subscripts, etc.) For multiplication, you can either leave a space, or use *. So x* x = xx = x². Note that this is not the same as x without a space; that will get read as an entirely different variable! • If you need to enter a vector, enter an ordered list of components, so for A you can enter either A = (Az. Ay, A₂) = {Az, Ay, A₂}. Note that the system isn't great with multiplying through by overall factors, so it's better not to write e.g. o= (2A, 2A, 2A₂). + X .. 15 calc Opera Functi Symb Relati