which of the following is a potential function for F(x,y,z)= < y2 +y?ex?,x2 + 2ye*?,xy +...
9) Find the absolute maxima and minima of the function f(x,y) = x2 + xy + y2 on the square -8 < x,y 5 8
evaluate JJ. (< –Y) A. ) Integrate f(x, y, z) = x2 + y2 + 22 over the cylinder x2 + y2 < 2,-2 <2<3 (IL dx dy dz Feraluate
Let f(x, y) = x2 – yż and D= {(2,y) : x2 + y2 < 4}. Let m and M be the absolute minimum and maximum values of f over D respectively. What is m - M?
F(x, y, z) =< P, Q, R >=<-y +z,x-z,x-y> S: z = 9 - x2 - y2 and z>0 (9a) Evaluate W= $ P dx + Qdy + Rdz с
How to solve it? Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
(2) Let f(z, y)-xy +x-y be defined on the closed disk {(z, y) E R2 : z? + y2 < 4} of radius 2. (a) Find the maximu and minimu of Duf at (0,0) over all unit vectors u. (b) Find the maximum and minimum of Duf over all points in the disk(,y) E R2 r2 + y2 < 4} and all unit vectors u. (llint. Think of IvJF as a function ofェand y in the disk.)
Given the function 1 f(x,y) = answer the following questions. 36 - 16x2 - 16y2 a. Find the function's domain. b. Find the function's range. c. Describe the function's level curves. d. Find the boundary of the function's domain. e. Determine if the domain is an open region, a closed region, both, or neither. f. Decide if the domain is bounded or unbounded. a. Choose the correct domain. OA. 9 The set of all points in the xy-plane that satisfy...
Use spherical coordinates to calculate the triple integral of f(x, y, z) = y over the region x2 + y2 + z2 < 3, x, y, z < 0. (Use symbolic notation and fractions where needed.) S S lw y DV = help (fractions)
Determine the absolute maximum and minimum values of the function f(x,y) = xy-exp(-xy) in the region {0<x<2} x {0 <y<b} where 1 <b< . Does the function possess a maximum value in the unbounded region {0 < x <2} x {y >0}?
2. (10 pts The random variables X and Y have joint density function f(x, y) == 22 + y2 <1. Compute the joint density function of R= x2 + y2 and = tan-1(Y/X).