Use the contour diagram for f(x, y) shown below to estimate the directional derivative of f in the direction at the point P. (a) At the point P = (2, 2) in the direction = 7, the directional derivative is approximately (b) At the point P = (2, 3) in the direction = j, the directional derivative is approximately (c) At the point P = (1,4) in the direction 7 = (i + 7)/√√2, the directional derivative is approximately (d) At the point P = (1, 0) in the direction, the directional derivative is approximately 4.8 4 3.2 2.4 1.6 0.8 0 of -0.8 2.0 -0.8 0.0 O 0 0.8 1.6 X 10.0 2.4 12.0 -2.0 3.2 16.0 18.0 14.0 8.0 4 (Click on graph to enlarge) 4.8

Q: Find fyyzz if f(x, y, 2) = cos(3y + az). Then evaluate fygazz at point (, 0, 4). COS

A: *Use chain rule

Q: 1. At the point (1, -1), the function (z,y) has a derivative of b in the direction toward (3, 1) and…

A: Given  that at the point (1,−1), the function f(x,y) has a derivative of 5 in the direction toward…

Q: y - 2)2 + (x-2)2 . Find the direction of heat flow in the plate at the point (2, 1). Heat flows in…

A: Introduction: The gradient of the temperature function at the point is the direction of the greatest…

Q: he surface al derivative

A:

Q: A circular disk of radius 5 meters centered at the origin has been unevenly heated. The temperature…

A: To find where the temperature on the disk is the greatest, we need to find the maximum value of the…

Q: Let f(x, y) = x² + y²¹e²+3. Find the directional derivative at (−3,−3) in the direction û =…

A:

Q: Q2 / Find the directional derivative of f(x.y.z) 4xy +5xz2 +6yz2 At the point P(3,1,4) in the…

A: ∂f∂x=4y+5z2∂f∂x=84∂f∂y=4x+6z2∂f∂y=108∂f∂z=10xz+12yz∂f∂z=168Therefore, the gradient is∇f (3, 1, 4)…

Q: -S) The height function of a very stronge moontador given by h(x,y) = 2xy + y² is You which…

A:

Q: (d) Find the directional derivative of f at (-2,1), in the direction of (-3,5).

A: Given f(x,y)=9-x2-y2 fx= -2x fy=-2y ∇f(x,y)=<fx,fy>=<-2x,-2y>…

Q: The temperature on a cubic box [0, 4] × [0, 4] × [0, 4] (measured in meters) can be described by the…

A: Function, Tx, y, z=x2y+y2z

Q: Find the direction in which the directional derivative of f(x, y) = x? + sin(xy) at the point (1,0)…

A:

Q: Given that Vf(2, -13) = 2i- j, find the directional derivative of the function f at the point (2,…

A: The given problem is to find the directional derivative of the given function at point (2,-13) in…

Q: EFGH is translated 6 units to the left and 3 units up. y -1 1 2 3 4 5 6 7 8 x E(4, -1) H(6, -2) -1…

A: Initially coordinates of F are (0,-3) After translating 6 units to the left, coordinates of F will…