If f is a scalar field and f, g are vector fields, then f f, f · g, and f × g are defined by the following. (f f)(x, y, z) = f(x, y, z) f(x, y, z) (f · g)(x, y, z) = f(x, y, z) · g(x, y, z) (f × g)(x, y, z) = f(x, y, z) × g(x, y, z) find an identical expression, assuming that the appropriate partial derivatives exist and are continuous.

The head librarian at the library of congress has asked her assistant for an interval estimate of the mean number of books checked out each day. the assistant provides the following interval estimate: from 740 to 920 books per day. what is an efficient, unbiased point estimate of the number of books checked out each day at the library of congress?

The data represents the semester exam scores of 8 students in a math course. {51,91,46,30,36,50,73,80} what is the five-number summary?

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