2. Let closed curve C consist of the line segment from (0, 0) to (2, 1), followed by the line segment from (2, 1) to (-1,1), followed by the piece of y = 2² from (-1,1) to (0,0). Also, let F = ( – 1, x²y²). a) Find F.T ds by integrating F over each piece of C and adding the results.

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Q: e Divergence Theorem to evalu (4x + 10y + z²) dS Js

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Q: 9. Find all the second partial derivatives of Z; given: a) Z = xy³In(3xev ) b) Z = Arctan ( x² /y³)

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A: compute ∫C F · dr for the oriented curve specified. F(x, y) = (ey^-x, e2x), piecewise linear path…

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A:

Q: 6. Set up but do NOT evaluate Evaluate the line integral 2 curve (t) - (t", t), where 0sts0. L ds,…

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Q: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

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A: We have to find the equation of  tangent plane.

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A:

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A: Use Green theorem.

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A:

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Q: Find the requested partial derivative. dz z= (3x +4y) ; (2,5)

A: Option D is the correct option. Use the chain rule to find the partial derivative for z w.r.t x.

Q: 4. Curl of f (x, Y, z) = 2xyi + (x² + z²)j + 2zyk is

A:

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A: Let's find.

Q: Let f(x, y, z) = ln(x2 + z) + y2exz − cos(2yz). Find fzyx.

A:

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A: Given problem is :

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Q: Assume that z = ƒ(x, y), x = g(t), y = h(t), ƒx(2, -1) = 3, and ƒy(2, -1) = -2. If g(0) = 2, h(0) =…

A: We use the partial derivatives to find dz/dt  Then plug x=g(t) and y=h(t)

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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Q: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

A:

Q: Find ôw/as and ôw/ôt using the appropriate Chain Rule. Function Values w = sin(7x + 8y) X = s + t, y…

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Q: Find the indicated partial derivatives of: 2х — 2у - f(x, y) = 2х + 2y at the point (x, y) = (1,3).…

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Q: Suppose that z = f(x, y) is differentiable at the point (64, 1024) withf, (64, 1024) = 3 and dz…

A: Topic:- partial derivative

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Q: Find the total differential for the function w = 13z ysin x. dw = 13z ysin xdx-13z sin xdy-26z ysin…

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