a) Compute the work done by F = (y², sin(z), x) along a straight line from (0,3,0) to (1, 0, 1). b) Compute the work done by F= (y², sin(z), x) along a triangular path from (0,3,0) to (1, 0, 1) to (0, 0, 2) and back to (0, 3,0). c) Compute the work done by = (x, y², sin(z)) along a circular path of radius 3, centered at (0, 1, 0), in the plane y = 1, counterclockwise when viewed from the origin.

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A: Given function is fx, y, z = xy2-x2z+yz2-z-11

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A:

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A:

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A: Find

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A:

Q: Q and Z are vector valued functions Q(-1) = , Q'(-1) = , Q''(-1) = Z(-1) = , Z'(-1) = , Z''(-1) =…

A: Given Q and Z are vector valued functions such that:Q-1=0,0,-2Q'-1=1,-1,-1Q''-1=3,2,-2 and…

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A:

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A:

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A:

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: he surface al derivative

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A: The complete solutions are given below

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A: Since you have posted multiple question in this question which are nt interlinked so i have solved…

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A: x^2y''-2xy'+2y=0; y1=x, y2=x^2 Verify that y1 and y2 are linearly independent

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A: The given function is  f(x, y, z) = y5 + xz

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A:

Q: i) P(5, 25) belong to y = x, what will the point P be transformed to after the equation transforms…

A: Real valued function

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A: To find A vector that gives the direction of maximum rate of increase.

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A: Given query is to find indicated partial derivative.

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

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Q: Show that fi (x) = cos x , f2(x) = cos 2x are orthogonal on [-7,71]. %3D

A: This is a application of integration problem

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Q: 2) r(1) = ti –t j-tk, t20 Draw the graph of the vector-valued function, explaining it in detail.

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Q: Consider the complex function f(z)= 1/(z^2 +1)  Find the residue of f(z) at the pole z=i.

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