Find the rate of change of f(x,y,2) = In(x + y + 2) – ryz in the direction from (-1,1,1) to (2,1,5) with respect to the distance measured at (-1,1,1) What is the maximum rate of increase in (-1,1,1) ?

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: 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: Find the maximum rate of change of f(x,y)= e^x^2 at (3,0) and the direction in which it occurs.

A: GIVEN DATA : Function fx,y=ex2        TO FIND : Maximum rate of change at 3,0 and the direction  The…

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A: Note: where △f(x,y) = ∂f∂x,∂f∂y

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A:

Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

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A:

Q: Find the rate of change of f(x,y) = In(x +y +z) – xyz in the direction from (-1,1,1) to (2,1,5) with…

A: solve:

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: F(X, y,z) = 2x -y? +z?

A: F(x,y,z)= 2x-y^2-z^2 at point (4,-4,2) df/dx= 2 df/dy=-2y df/dz= -2z

Q: Find the rate of change of f(x,y,2) = In(x + y + 2) – xyz in the direction from (-1,1,1) to (2,1,5)…

A: To find the rate of change we need to determine the directional derivative: The expression for the…

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: Find the direction 0 in which the directional derivative of the function x + y f(x, y) = 2(x + y) -…

A: Given that: f(x, y)=2(x+y)-x+yxy

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A:

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) 3 x2 + y2 + z2 (7,…

A:

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

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z)…

Q: What is the linearization L(x, y) of a function f (x, y) at a point (a, b)? How is L(x, y) connected…

A: Linearization L(x,y) of a function f(x,y) is given by the formula

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² I in the…

A:

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

A: Consider the function: fx,y,z=xlnyz Differentiating with respect to “x” then,…

Q: (2) Let f(x, y, z) = xy + yz + x²z². What is the maximum rate of change of f at (1,2, 3)?

A:

Q: Find the maximum rate of change of f(x, y) = ln(x² + y²) at the point (3, 5) and the direction in…

A: Here is the solution of the given problem. Unit Direction:

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A:

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 rate of change of f(x,y,2) = In(x + y + 2) – ryz in the direction from (-1,1,1) to (2,1,5)…

A:

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

A:

Q: The temperature at any point (x, y) in a steel plate is T = 500o - 0.5x2 - 1.2y2, where x and y are…

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A: Given function is

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

A: The given function is: f(x,y)=8yx

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A: The maximum rate of change of given f(x,y) at point (4,9) is,

Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…

A:

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: 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 the maximum rate of change of f(x, y) = ln(x² + y²) at the point (-4, -4) and the direction in…

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Q: 2. Find the derivative of f(x, y, z) = x³ - xy2 - z at Po(1,1,0) in the direction of V = 2ỉ – 3j +…

A:

Q: The temperature at any point (x, y) in a steel plate is T = 500 - 0.6x2 - 1.2y2, where x and y are…

A: Partial differentiation with respect to x. Treat every other variable as a constant.

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

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Q: Find the rate of change of f(x,y) = In(x +y+ z) – xyz in the direction from (-1,1,1) to (2,1,5) with…

A: Given problem is :

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Q: Compute the directional derivative of f(x, y, z) = y²e*y% at the point (0, 1, -1) in the direction…

A: We will find out the required value.

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

A: We have to solve

Q: Find the direction of the maximum rate of increase of f(x,y, z) = y²sinxz² at the point (0,3, –1).…

A: Given the function f(x,y,z)=y2sin(xz2) And the point (0,3,-1)

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) + y2 + z2 (3, 7, 2)…

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Q: The average rate of change of the function f(z) = 13z +4 on the interval [1, 4] is

A:

Q: Find the maximum rate of change of f(x, y) = In(x² + y²) at the point (3, 5) and the direction in…

A: This is a problem related to the derivative of the function. For calculating the maximum rate of…

Q: Find the gradient of tangent to 3 x2 - x y – y = 23 at the point (3, 1). Enter the exact value of…

A: We have to solve given problem:

Q: Find the rate of change of f(x,y,2) = In(x + y + z) – xyz in the direction from (-1,1,1) to (2,1,5)…

A: The gradient vector to the given scalar function is:…