7. Which transformation of (x, y) is a dilation? (F) (3r, y) (G) (-y, 2) (H) (3z, 3y) (J) ( + 3, y +3)

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

A:

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: Find the first partial derivatives with respect to x, y, and z and evaluate each at the given point.…

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Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: f(x,y)=x² +16xy + y² +8

A:

Q: If f(x, y, z) = 4zy", then the gradient at the point (5, 4, 5) is V f(5, 4, 5) =

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

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

A:

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: 8 Find the linearization L(x, y) of the function at the given point f(x, y)=1+xIn(xy-5), (2,3)

A: Given: f(x,y)=1+xln(xy−5)(2,3)L(x,y)=?

Q: How is the linearization of f(x, y) centered at (a, b) defined?

A: To define linearization of a function f(x,y) at point (a,b).

Q: The gradient vector of the function f(x, y, z) = ln(yz) - x² is: Select one: ○ (−2x,, 1) O None of…

A: To find the gradient vector of the functionf(x, y, z) = ln(yx)-x2

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

A:

Q: Find the gradient of the function at the given point. In(x² – y) - 9, (3, 8) z = Vz(3, 8) =

A:

Q: 5) Find the gradient of o = x?yz + 4xz2 at (1, -2, -1).

A:

Q: Find the gradient of the function at the given point. In(x² – y) – 6, (3, 8) z = Vz(3, 8) =

A:

Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: (2x, /, // ) (2x, -, -…

A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .

Q: g(x, y) = 6x² – 3y², (/8, /5) Gradient is f(r, y) = tan 6y (16, 2) Gradient is

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Q: The gradient vector of the function f(x, y, z) = ln(yz) + x² is: Select one: ○ (2x,-1,-1/2) (2x₂ O…

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Q: Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+…

A:

Q: How many second partial derivatives does f(a,b,c, d) have?

A: Let p=fa,b,c,d. Note that, for a function of two variables p=fa,b there are four second partial…

Q: Integrate f(x, y, z) = x2 +y – z over the line segments from (0, 0, 0) to (1, 0, 1)  and then to the…

A: According to the given information, it is required to integrate the function over the line segment.…

Q: Find both first partial derivatives. f(x, y) fx(x, y) = fy(x, y) = ху ,2 x + ,2

A: Find the partial derivatives

Q: Compute the partial derivative fa(, 4, 2) of the function f(2,4, 2) = yz' + 2 – 2 vy + * +2 y. O…

A:

Q: Find the gradient of the function at the given poin In(x² - y) -2, (3,8) X Vz(3, 8) = Z =

A: We are asked to find the gradient of the function.

Q: Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

A: use partial derivative for finding the gradient.

Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: Find the maximum rate of change of f(z, y, z) = tan(6z + 2y + 3z) at the point ( – 1, 3, – 2).

A: We need to find maximum rate of change.

Q: 3. Find the partial derivatives of f(r, Y, x) = r³yz² + 2yz. %3D

A:

Q: Find the rate of change of f (x, y, z) = 3xyz in the direction normal to the surface yx² + xy² + yz²…

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

A: The given function,   z=lnx2-yx-3, at the point 3,8

Q: Find the Linearizat ion of Non lineah Relations hip Y= (ax+

A: This is the problem of linearization, application of differential calculus.

Q: Find all the first partial derivatives of z = 5x°y - 8xy*. (Choose all applicable answers.) O zz =…

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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: Letf(x, y,z) be a function with the gradient vector . What are the extreme points of f with…

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Q: Letf(x, y,z) be a function with the gradient vector . What are the extreme points of f with…

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Q: 3. Evaluate the gradient of S(1, y, 2) = In(cosh z+ y) - arctan| at (1,y) = (7/2, 1).

A: Given that fx,y,z=lncosh x+y-z2 arctanx2y2+z2 To find the gradient of f(x,y,z) :…

Q: Compute the partial derivatives. z = x5 - y6 əz 1 5x - ,6 dz ду II II

A:

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

A: for finding gradient we have to find the derivative with respect to x and y   z  = ln(x2 -y)/x - 3…

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

A:

Q: Calculate the partial derivative f2(3,3,1), where f(x, y, z) = xyz. %3D

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Q: tor. f(x,y)= In (8+3x²+3y²); P(3,-1); (3.2) d the gradient of f(x,y) = In (8+3x²+3y²). xx,y)=

A: Topic:- application of derivatives

Q: Find the linearization of f(x,y) at the indicated point (Xo.Yo). f(x,y) = In (x +y): (4, 5) L(x,y) =

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Q: Find the linearization of f(x,y) at the indicated point (X0:Yo). f(x,y) = In (x +y); (6, 1) L(x,y) =

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Q: The temperature T(x, y, z) is given by T(x,y,z) = 4x2 − y2+ 16z2. In which direction T increases…

A: We have to find the maximum rate and the the direction where T increase

Q: Find the first partial derivatives of 2х — 4у - f(x, y) = at the point (x, y) = (2,2). 2х + 4y af…

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

A: