Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = (cos(z) + xy2) i + xe−z j + (sin(y) + x2z) k, s is the surface of the solid bounded by the paraboloid z = x2 + y2 and the plane z = 4.

Multiply. −2x(6x4−7x2+x−5) express the answer in standard form. enter your answer in the box.

To find the extreme values of a function f(x. y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x, y)=xy

Kathy spent 5/8 of her money on books and another 1/6 of her money on stationeries. what fraction of kathy’s money was left?