Q2) a) Find Maclaurin expression of f(x) = Cosh (x) b)Find the gradient of the function f(x, y,z) = x2 +y3 – 2z + z In x at point P (2, 2,1)

Q: find the gradient of the function and the maximum value of th directional derivative at the given…

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Q: 1-Find the gradient of (1) f (x,y)= In(x²+y²) (1,1)

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Q: Find the gradient of the function z = cos(x2 + y2), at the given point (3, −4)

A: Given=z=cos x2+y2 at point x,y=3,-4Gradient∇x,y=fxx,yi+fyx,yjwhere fx,y=z=cos x2+y2

Q: Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to (-1, 0,…

A: By Fundamental theorem line integral,we have Where C is curve joining to

Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: Find the gradient of the function f(x, y, z) = xeyz, and the maximum value of the directional…

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Q: If the gradient of f(x, y, z) at (1, 2, 3) is 2i – 2j +k, then the maximum value for a directional…

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Q: Find the gradient of f(x,y,z) = (x² + y² + z²) Vf|(−2,2,− 1) = ₁ + Oj + k (Type integers or…

A: We want to find the gradient of the given function at point (-2,2,-1).

Q: .    Find work done by the gradient of f(x, y, z) = zexy- 2y2/z  along the path from (1, 2, 4) to…

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Q: Find the maximal value of the directional derivative of w = xy°z at the point (2, 1, 1)

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Q: Choose the gradient of the function f defined by f(x,v,z) = cos(xy +9xz + 13yz). O sin(xy O -cos(…

A: Take gradient and solve

Q: .    Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to…

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Q: Find the gradient of f(x,y.z)= (x2 + y2 + z2) - 1/2 + In (xyz) at the point (1,- 2, - 2) %3D Vf (1.…

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Q: Given : 6 (x, y, z) Compute the gradient 3 6y³z³ - 5 ex at = PA (2,2,1.5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

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Q: Find the gradient of f(x, y) = y ln x + xy2 at the point (1, 2).

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Q: Find the gradient of the function w = xy2z2,  and the maximum value of the directional derivative at…

A: Given function:    w=xy2z2

Q: 5. Find the gradient of cos(xy) – 3y* + 3 at the point (1,4)

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Q: Find the gradient of the function z = ln(x2 − y) /(x − 4), at the given point     (2, 3)

A: To find the gradient differentiate z partially with  respect to x and y. Given function  z=lnx2-yx-4…

Q: 8. Find the directional derivative of f (x, y, z) = xyz3 at P(2, 1, 1) in the direction of Q(0,…

A: Ans=1 I have considered image question bcz I think you have done mistake while typing... Now go…

Q: The gradient vector of the function f(x, y) = sin(4x - 6y) is (4 cos(4x - 6y), 6 cos(4x - 6y)).…

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Q: Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

A: Given  G(x,y,z)=6y2z3-5e-x We have to find the gradient at the point PA(2,2,1.5)

Q: Find the gradient of the function f(x, y, z) = √(x2 + y2 + z2), and the maximum value of the…

A: The given function is fx,y,z=x2+y2+z2

Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

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Q: Find work done by the gradient of f(x, y, z) = zexy+ 2y2z  along the path from (1, 2, 4) to (-1, 0,…

A: The gradient of f(x, y, z) is:

Q: Compute the gradient of the function at the given point. f (x, y, z) = In(x² + 7y – 3z²) ; (7,7,7) O…

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Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (7, 15,-5) Vw(7, 15,-5) =…

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Q: The gradient of f(x, y) = e³ ² sin(3 - y) at (x, y) = ( - 1, – 3) is defined as followed: V f(а, у)…

A: It is gradient vector by using partial derivative

Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) 2, Vw(10, 5, -2)…

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Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: The gradient of f(x, y) = xy at (x, y) = (3, 1) is

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Q: First, compute the gradient of the function p(x,y)= 12- 2x-y Then evaluate it at the point (- 1,2).

A: We need to find partial derivatives with respect to x and y to find gradient

Q: 8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

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Q: Find the gradient of the function and the maximum value of the directional derivative at the point…

A: The solution is given as

Q: Find the gradient of the function at the given point. In(x2 - у) - 3, (2, э) Vz(2, 3) = %3D

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Q: 2 - What is the directional derivative of the function f(x, y, z) = x° - 2xy + z point A, = (1,1,0)…

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Q: Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0,–3,5)

A: Solution: The objective is to find the directional derivative of the given function

Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: The gradient of f(x, y) = ry at (x, y) = (3, 1) is %3D

A: Explanation and solutions is given below....

Q: The gradient of f(x, y) = xy at (x, y) = (3, 3) is

A: Given problem:- Find the gradient of f(x, y) =xy at (x, y) =(3, -3)

Q: What is the rate of increase of the scalar function f(x,y,z) = sin (πx/3) sin (πy/2) e^-2z from the…

A: See the attachment

Q: Find the gradient of the function f(x, y) = (x + y)/(y + 1),and the maximum value of the directional…

A: Given: fx,y=x+yy+1 The gradient of fx,y can be calculated as, ∇fx,y=i^∂∂xfx,y+j^∂∂yfx,y Here,…

Q: Compute the gradient of f (x, y) = (x + 2) + xysin(y) at (0, 1)

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Q: Find the direotional derivative of the scalar function f-x'+ y' +2z', at the given point (1,1,2), in…

A: Explanation of the answer is as follows

Q: What is the directional derivative of f(x,y,z) = ln(x²+2y²+ 4z²) at the point P(-1, 2, 4) in the…

A: The given function is; f(x,y,z)=ln(x2+2y2+4z2) Point P(-1,2,4) u=-3i/13 -4j/13 -12k/13.

Q: Find the work done by the gradient of ƒ(x, y) = (x + y)2 counterclockwise around the circle x2 + y2…

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