Suppose F(x, y) = (2y, - sin(y)) and C is the circle of radius 6 centered at the origin oriented %3D counterclockwise. (a) Find a vector parametric equation 7(t) for the circle C that starts at the point (6, 0) and travels around the circle once counterclockwise for 0 <1< 27. F() = (b) Using your parametrization in part (a), set up an integral for calculating the circulation of F around C. F. dr = FG0) F) dt = dt with limits of integration a = and b = (c) Find the circulation of F around C. Circulation =

Q: Find the point where the tangent line to the curve 7(?) = (V? +3,ln(?² +3),t) at (2, In 4,1) 5. %3D…

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Q: 5. (a) (b) The surfaces (x - 2)² + z² = 9 and y = z² intersect along the curve C. Find a vector…

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Q: Match each parametrization with the corresponding surface. (i) (ii) (iii) (iv) (v) Answer Bank (u,…

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Q: Suppose F(x, y) = (2y, — sin(y)) and C' is the circle of radius 5 centered at the origin oriented…

A: The given vector field is F→x, y=2y, -sin y. The curve C is the circle of radius 5 centered at…

Q: F(x, y) = (2y, – sin(y)) and C is the circle of radius 5 centered at the origin oriented…

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Q: a) By first sketching its projection onto the yz-plane, sketch the curve r(t) = (t, cos(t), 2…

A: For (a), We will plot the sketch of r(t)=t, cos(t), 2 sin(t),  0≤t≤4π onto the yz-plane (that means…

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: (a) Find a vector parametric equation for the ellipse that lies on the plane x + 3y + z = 5 and…

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Q: Solution r(t) = 6 cos(t) i + 6 sin(t)j + 3tk. The parametric equations for this curve are x= y = 6…

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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: 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: The path r(t) = (t- sin t) i+ (1- cos t) j describes motion on the cycloid x=t- sin t, y=1- cos t.…

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