8) a) About how much will f(x,y,z) = xy?z? change if the point (x,y,z) moves from...
8) a) About how much will f(x, y, z) = xy3z2 change if the point (x,y,z) moves from (3,-7,-6) a distance of ds = 0.5 units in the direction of 2ỉ+ 2j - 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.)
What is the instantaneous rate of change of z = f(x,y)=x² + xy(with respect to horizontal distance) at the point (2,1) if one is heading directly toward (4,-2)? -8 -3 4 12 b) c) d) e) none of these 113 113 V13 113 a) o What is the average rate of change of z = f(x, y) = x² + xy(with respect to horizontal distance) as one travels from (2,1) to (4,-2)? 2 5 12 c) d) e) none of...
Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 5 sin(xy), (0,8) maximum rate of change direction vector
(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:
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
(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
Find the area of the lateral surface over the curve C in 6. the xy-plane and under the surface z - f(x,y) f(x,y)-h, C:y-1 -x2 from (1,0) to (0,1) Surface: Lateral surface area - f(x, y) ds z =f(x, y) Lateral surface xy) As C: Curve in xy-plane Find the area of the lateral surface over the curve C in 6. the xy-plane and under the surface z - f(x,y) f(x,y)-h, C:y-1 -x2 from (1,0) to (0,1) Surface: Lateral surface...
Find the directional derivitive of f(x, y, z) xy at the point (4,1,1) that goes in V=2i-j+2k direction.
Find the directional derivative of f(x,y,z)=xy+z^3 at the point (2,3,1) in the direction of a vector making an angle of 3π/4 with ∇f(2,3,1).