3 Consider the function f(x,y,z) = Зхyz - 2 the point P(0, - 3, – 2), and the unit vector u = 7' 7' a. Compute the gradient off and evaluate it at P. b. Find the unit vector in the direction of maximum increase of f at P. c. Find the rate of change of the function in the direction of maximum increase at P.

Q: Compute the directional derivative of the following function at the given point P in the direction…

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Q: Consider the following. xY,z) = Vx+ yz. Р(1, 3, 1), (a) Find the gradient of f. Vfx, y, z) = (b)…

A: Given that                   f(x,y,z)=x+yz                   P(1,3,1)                  u=(67,27,37)…

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Q: I. Draw a contour map of z = Vx2 + (y – 2)2 using k = 0, 1, 2, 3, 4, then sketch its graph in R³.…

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Q: Find the gradient of the function f(x, y, z) = yz², at the point (0, -1,–1) V f(0, –1, –1) =

A: fx, y, z=yz2 & the point is 0, -1, -1. Partially differentiating with respect to x, we get fxx,…

Q: 1) For f(x,y, z) = x² – (1 – y)² + z². Find directional derivative of f at P(1,1,1) in the direction…

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

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Q: Find the gradient of the function f(x,y,z) = x2 + y3 - 2z + z In x at point P (2, 2,1) %3D

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Q: Find the gradient of the function f(x, y, z) = zy?, at the point (0, 1,-1) V f(0,1, –1) =

A: We have to find the gradient of the given function at the required point.

Q: (a) Find the directional derivative of f at (0,1) in the direction of the vector i = i+27. f(r, y) =…

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Q: Determine the gradient of f(r, y) = ez sin(5y) at (r, y) = (3, – 1). Round to 2 decimal places. V…

A: Given query is to find the gradient at indicated point. Given is the function  f(x,y)=e5xsin(5y).…

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A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Suppose n is a vector normal to the tangent plane of the surface F(x,y,z) =0 at a point. How is n…

A: For the following gradient vector,

Q: 2. Let T(x; y) = sin(2x – y) , P (-; ) and Q(0;0) (a) Determine the directional derivative of T at P…

A: Tx,y=sin2x-y, P=-π3,π6,?=0,0                                      P1  P2                ?1,…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y² + z2 (5,…

A: I have calculated upto eq (1) above because it is easy to calculate max value from there. You do…

Q: 2. Find the gradient of the function f(r.y) In(r y²) at the point( 1, 1).

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Q: Let a be a real number and f(x, y) = 2ax2y + 3xy. Let v 3i – j and let V f(x, y) denote the gradient…

A: From the basic vector calculus

Q: 3 2 6 Consider the function f(x,y,z) = e xyz -6, the point P(0, – 3,1), and the unit vector u = 7'…

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Q: Consider the function f(x.y,z) = 3x +y +z? + 3, the point P(2,0,4), and the unit vector u = a.…

A: Use gradient formula and magnitude to solve this

Q: Find the gradient of the function f(x,y,z)=y^(2)ln(xz), at the point (1,−1,e) ∇f(1,−1,e)=?

A: Given query is to find the gradient of f(x,y,z) at a point (1,-1,e).

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Q: Consider the function f(x.y.z) =x + 2y? + 3z? +2, the point P(4,0,4), and the unit vector u = a.…

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Q: Consider the function f(x, y, z) = xy + y² +². (a) What is the gradient grad f of f, and what is its…

A: (a) Consider the given function, fx,y,z=xy+y2+z2 Here we need to find the gradient of f and its…

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A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 01. (a) Find the gradient of f(x.y.2) = (r+ 2y + 32)i at the point (1.1.2) (b) Find the directional…

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Q: Find a unit vector in the direction in which f (x, y, z) = 3x³z² + 3y°z + 24z – 4 increases most…

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Q: Find the directional derivative of the function f(x, Y, z) = x + ln(y² + z²) at the point A(2,1, 1)…

A: To find the directional derivative of the function f(x,y,z)=x+ln(y2+z2) at point A(2,1,1)  in the…

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Q: 1. Find the gradient of the following functions at the given point and hence find the directional…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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Q: 1. Consider the function z= f (x, y). a. Give the formula for the gradient at P= (a, b). b. Give the…

A: Consider the given information.   (a) The given function is z=f(x,y) and the point is P=(a,b).…

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Q: : (x² + y²)e-(x*+y -5), Find the rate of change of f at X = (1, –2) in the direction V pointing…

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A: The given function fx,y,z=y2ln(zx)

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Q: Let a be a real number and f(x, y) = 3ar?y + 8ry³. Let v = 3i – j and let Vf(r, y) denote the…

A: This question is simply based on formula of gradient

Q: . Use the gradient vector to find the directional derivative of f (x, y) = at x2-y the point (1, 2)…

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Q: Consider the function f(x.y.z) = 4x + 4y + 2z? + 4, the point P(1,0,4), and the unit vector u= a.…

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Q: Consider the following. (x, y) = x/y, P(8, 1), u (a) Find the gradient of f. V(x, y) = (b) Evaluate…

A: F(x,y)=xy at P(8,1), u=35i^+45j^∂F∂x(x,y)=∂F∂xxy                =1y∂F∂x(8,1)=1∂F∂y(x,y)=∂F∂yxy…

Q: Given function f(x, y) = xy² - x² + 5y. a) Find the maximum rate of change of f at the point (1, -2)…

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Q: 5. Consider the function f (x, y, z) = x2 + 2y2 + 4z2 + 10; the point P(1,0,4); and the unit vector…

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Q: 1. Find the gradient of the function f(x, y) = x² sin y. 2. Find the rate of change of the function…

A: The given function is;  f(x,y)=x2 Siny.

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Q: 4. Let f be a differentiable function of two variables with f(0, 4) = 0 and Vf(0, 4) = (2, v3). (a)…

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Q: Consider the function f(x,y, z) = Ty + y² + 2². %3D (a) What is the gradient grad f of f, and what…

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Q: Let f(x, y) = x /G. At the point (1, 4), find a vector (a) In the direction of maximum rate of…

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Q: Consider the function f(x,y,z) = 3x +y+z +4, the point P(3,0,1), 1 1 ,0, V2 and the unit vector u =…

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