Evaluate f. f(x,y) ds where C is the piecewise curve composed of the line

Q: Find an equation of the tangent plane at the given point: (2,1) F(r.a) 3²-3,

A: Since you have posted a multiple question according to guidelines I will solve first question for…

Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

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Q: What is the image of a horizontal line y = k € R under the mapping W = 2²?

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Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: Let L be the line through the point Q = (- 6, - 9, - 10) and direction vector d = [- 1, - 2, - 2]^T.…

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Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x2, xy), line segment from (0, 0) to (2,…

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Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: Find the distance from the point (0,1,-1) to the line a(t) = (-2, 2, 4)t + (-6, - 1,5)

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Q: Evaluate f (5ydy + 3xydx) C if C is the closed curve determined by the x-axis, the parabola y = x²…

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

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Q: t G(u, v) = (6u + v, 32u + 9v) be a map from the uv-plane to the xy-plane. Find the image of the…

A: We have to find the equation of line in slope intercept form.