8) a) About how much will f(x, y, z) = xy3z2 change if the point (x,y,z)...
8) a) About how much will f(x,y,z) = xy?z? change if the point (x,y,z) moves from (3.-7.-6) a distance of ds = 0.5 units in the direction of 21 +27 - K? b) Find the maximum change in f(x,y,z) in moving 0.5 units away in any direction, and indicated in what direction this occurs.
By about how much will f(x,y,z) - In +y? +2? change if the point P(x,y,z) moves from Po(4,3,9) a distance of ds = 0.1 unit in the direction of 31 • 61 - 2 ? The change in value is about do (Round to four decimal places.)
(1 point) Find the maximum rate of change of f(x,y) = ln(x2 + y²) at the point (-2,-5) and the direction in which it occurs. Maximum rate of change: Direction (unit vector) in which it occurs:
please circle the answer! (1 point) Suppose f (x, y) = , P = (1, 3) and v 3i - 2j A. Find the gradient of f Vf = i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) it j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf...
6 (15%). Find the rate of change of f(x, y, z) = x/(y + 22) when we move away from the point (4, 2, 1) in the direction (3, 4).
For the function f(x,y,z)==xyz and the point P=(-1, 8, 2): a) Calculate the gradient at P. Vf(-1, 8, 2) = b) Find the rate of change in the direction v=(2, 2, - 1) at P. D.f(-1, 8, 2)= c) Find the maximum rate of change of f at P. MAX RATE OF CHANGE =
(1 point) Calculate ſls f(x, y, z)ds For y = 4 – z2, Is $(x, y, z) ds = 0 < x, z <7; f(x, y, z) = z
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e-x-2y-2? where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -1, 2) in the direction toward the point Q(3,-3,3). Answer: Dp S(2.-1, 2) = 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
(1 point) The plane x y + 2z = 8 intersects the paraboloid z = x2 + y in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin. Point farthest away occurs at ). Point nearest occurs at (1 point) The plane x y + 2z = 8 intersects the paraboloid z = x2 + y in an ellipse. Find the points on this ellipse that are nearest to and farthest from...
The directional derivative of a function f(x, y, z) = 2x²yz - 100 at the point Po(1,-1,-1) in the direction of a vector v = 2i + 2j + k is Select one: 2 A. 3 B. 2 C. D.O. E. None of these answers