Let Fâ =(7z+3)iâ +4zjâ +(9z+9)kâ , and let the point P=(a, b,c), where a, b and c are constants. In this problem we will calculate div Fâ in two different ways, first by using the geometric definition and second by using partial derivatives. Consider a (three-dimensional) box with four of its corners at (a, b, c), (a + w, b, c), (a, b + w, c) and (a, b, c + w), where w is a constant edge length. Find the flux through the box. flux = Thus, we have div F Vector (x, y, z) = lim w Right arrow 0 Next, find the divergence using partial derivatives: div F Vector (x, y, z) = .

More challenges: 1) factor out the indicated quantity.8mn² + 7mn - m : factor out the quantity -m2) factor the polynomial by grouping.2vw + 7cv + 14cw + 49c²3) factor completely using the difference of squares along with factoring by grouping.25v³ - 25v² - 4v + 44) factor the sum of cubes. 125x³ + 645) q³ + 27r³6) factor completely. use difference of squares.729p^6 - 6^67) solve the equation(7x + 4)(9x - 1) = 08) a. find the values of x for which f (x) = 0b. find f (0)f (x) = x² + 2x - 489) find the x and y-intercepts for the function defined by y = f (x)f (x) = (x + 3)(x + 4)(x - 1)²10) factor the trinomial completely by using any method. remember to look for a common factor first. 3v² - 2v - 16