Find curl F if F(x,y,z) = 16yºzº i - 8x³z8j - 7xy4 | curl F = (-28xy3 + 64x³z7) i+ (7y4 + 80y5zª)j+ (-24x²z® - 80y^z5) k curl F = (-28xy3 + 64x³z7) i + (7y4 + 80y5z4)j + (24x²z8 + 80y4z5) k O curl F = (-28xy3 + 64x³z7) i + (7yª + 80y524) j + (24x²z8 - 80y^25) k curl F = (28xy3 + 64x³z7) i+ (7yª + 80y5z^)j+ (-24x²z8 - 80y^z5) k

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

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A:

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A:

Q: Find all the second partial derivatives. T-е-бг сos(0) Trr Tre %3D Ter Тө II II II

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

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A: Given vector is (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

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

A: given,          any function fx,y at a,b

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A: Given, The function f(x,y). It's gradient is given by, For example,

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A:

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.…

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A:

Q: ChainR ulef or PartialD erivativs

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A: Given the function fx,y,z=yex-x2sinz and the point 0,7,-3. Computing the partial derivatives,…

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A:

Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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A: We will solve the following partial derivative.

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A:

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

A:

Q: Choose the gradient of the function f defined by f(x, y, z)= In[1 + (17xy + xz +9yz)²].…

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Q: List the critical points of the function f(x, y) = (x − 1)³(y + 2)² for which the Second Partial…

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A: gradf =∇f =i∂∂x+j∂∂y+k∂∂zf .

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A:

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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 orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

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A:

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A: Given function: fx,y,z=xy2z3

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

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A:

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A: Let f = (x2y2)i^ - (z3y-4x)j^ + 4y2xk^

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Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

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A: