Compute the vector line integral: x – 4 dx + (x – 4)² + y² -y dy :- 4)2 + y² where C is the circle of radius 2, centered at (4,0) with the counter- clockwise orientation.

Q: Find the arc length of the space curve given by the vector equation r(1) = (- 9t + 16) + (-9² +…

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Q: Find a vector function r(t) that describes the curve of intersection be- tween the elliptical…

A: Given To find a vector function r(t) that describes the curve of intersection between the elliptical…

Q: Find the positive value for which the vector r(t) = (3t, 10t², 7t² – 2) is perpendicular to r'(t).

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Q: Suppose F(x, y) = x² + y² and C is the line segment from point A = (1, -1) to B = (3,-5). (a) Find a…

A: Given          Let       (a)   The equation of the line segment from A(1, -1) to B(3, -5) is,,…

Q: Let C be the upper half of the circle whose equation is x2 + (y - 2)2 that is generated by revolving…

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: Consider the following function. T: R? - R, T(x, y) = (2x?, 3xy, y²) Find the following images for…

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Q: 5. For f(x, y) 2x +y v 3i-4j find the rate of change of fat (1,2,6) in the direction of the vector =…

A: rate of change of the function at the given point along the given direction

Q: Suppose F(x, y) = x² + y²j and C is the line segment segment from point P = (-3,-4) to Q = (-3, 1).…

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Q: Let F(x,y, z) = rye" – 2² Jī and P(1,0, –1).

A: Given Fx,y,z=xyey-z2x and P1,0,-1Vector u=⟨2,-3,6⟩

Q: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

Q: Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector…

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Q: Calculate the divergence and the curl of this vector function.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the parametric equations of the line tangent to the curve of intersection of the surfaces x² +…

A: The tangent to the intersection of the curves: f(x, y, z)=0, g(x, y, z)=0 is parallel to the vector:…

Q: Find the derivative of f(x, y, z) = x3 - xy2 - z at the point po (2,1,0) in the direction of vector…

A: Given the function fx,y,z=x3-xy2-z at the point p02,1,0 in the direction of vector v=2i-3j+6k. Find…