Calculate the gradient, Vƒ, for the following scalar functions (a) ƒ = xyz. (b) ƒ = x² + y² + z². (c) f = xy + yz + xz.

Q: 1. f(x, y) = 1+ 2x/y, (3,4), v= 4î – 3ĵ |

A: According to our company policy we can answer only first question and rest can be reposted. Thanks

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: (a) z = x² + y² – 4x in P(1,2) (b) z = yln(x +y) in P(-3,4) %3D

A: a) Compute the gradient of z=x2+y2-4x in P1,2 as follows: It is known that the gradient is…

Q: Determine the stationary points of the function y = x2e-x and hence classify them.

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Q: The maximum value of directional derivative of f in the direction of b is given by .. (a)Vf.6 (b) Vf…

A: We need to tell the maximum value of the directional derivative of f in the direction of b^.  The…

Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: Find the gradient of the functions below a)f(x, y) = In Vx? + y?

A: Here we will find out the required value.

Q: Find the analytic function whose imaginary part is v =2xy

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Q: Let P= (x,y) be a point on the graph of y = x. Express the distance, d, from P to (7,0) as a…

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Q: Describe the two main geometric properties of the gradient V f.

A: A. If f is differentiable, then the dot product (∇f )x ⋅ v of the gradient at a point x with a…