c) By using Green's theorem evaluate $ (4.cy – y*) dx + (2³ + 3xy) dy where C is a closed curve starting from the origin to point (0,1) along SUTM -1 the y-axis, then to point \v2' v2) along the semi-circle = -P1 - y?, then on a straight line, back to the origin.

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: (1) Evaluate the line integral 4xy dx + (2x² – 3xy)dy if the curve C consists of the line segment…

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Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

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Q: Consider the curve C parametrized by (x, y) = (3 cos (-10t), 3 sin(-10t)), for –x/2sts a/2 Then C is…

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Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

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Q: Use Green's theorem to evaluate , (5xy + x2 + y?) dx + (x²-y)dy where C is a closed curve that is…

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Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

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Q: Consider the curve parametrized by a = e-sin(0) and y = ecos(8) for 0 ≤ 0 < 2π. At what points (x,…

A: The parametrized curve x=e-sinθ and y=ecosθ for 0≤θ&lt;2π.

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z =x²…

A: Tangent line to ellipse will be perpendicular to normals of both the surfaces Therefore,  The…

Q: What is the tangent plane equation of sphere f(x, y. :)=x² + y² += =6 at point (1,-1,2)? O a.…

A: I hope that this solution will help you .Thankyou. Best regards.

Q: Sketch the recion enclosed by the given curves. Decide whether to integrate with respect to rwr.Daw…

A: Draw all the regions first then decide which region satisfy all the curves

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: rea under the curve y = 2x – x² from x = 1 to x = 2 with n = 4 %3D tonglon

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Q: 1- Find all of the points where the curve r = 2 cos (-) intersects the circle of 3, radius v2…

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Q: c) By using Green's theorem evaluate $ (Ary – y*) de + (* + 3ry) dy where C is a closed curve…

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Q: C is the curve given (in three parts) by the arc of the circle x2 +y? the circle y² + z² = 4, x = 0…

A: According to the given information, it is required to determine:

Q: For which values of t is the parametric curve x=8t, y=t+t, -0c0s ts 00 concave up? (Enter your…

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: 6- Find the avea of the Surface of revolution genetaled by revalving the x-axis the arc abaut from…

A: To find - Find the area of the surface of revolution generated by revolving about the x-axis the arc…

Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)ĵ where C is the circle x² + y² =…

A: In this we have to verify green theorem.

Q: By using Green's theorem evaluate (4.ry – y') dr + (x + 3ry) dy where C is a closed curve starting…

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Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: (6) Suppose the closed curve C in R? starts at the point (-1, 1), goes along the parabola y = r? to…

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Q: 5. plot x?-y?=z (Elliptic paraboloid) in 3D.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Consider the parametric curve C given by X= √x= √2+ - cos t 2y = soin't where te [0.2π] (1)…

A: (1)Given,x = 32t-cos(t)y=5sin2(t)    where    t∈0, 2πcurve C has horizontal tangent line where dydx…

Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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Q: c) By using Green's theorem evaluate UTM £ (kry – y") dz + (z² +3ry) dy where C is a closed curve…

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Q: 56 Consider points P and Q in the x-y plane, with P = (1,0) and Q = (0,1). The line integral 2|(xdx…

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Q: B. Find the length of the circle of radius r defined parametrically by x = r(v1 – sin t) and y =…

A: We need to find the length of the circle which is parametrically defined as below.

Q: Use Green's Theorem to evaluate dr, where F-(VE+ 4y, 2+ C consists of the arc of the curve y 1z - z…

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Q: 3. Find a parameterization of the curve C= r(t) = (x(t), y(t)) a. Where C is the line segment…

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Q: Use Green's theorem to evaluate $ 2y3 dx – x3y² dy, where C is the positively oriented circle of…

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Q: Determine the surface of revolution if the arc y^3 + y = x^2 + 6x on the interval [−5, −1] is…

A: The curve will appear like this

Q: Let C be the curve of intersection of the parabolic cylinder x = 2y, and the surface 3z = xy. Find…

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Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: Use Green's Theorem to evaluate | F. dr, where F = (Va + 5y, 2x + Vỹ ) and C consists of the arc of…

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Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

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Q: 9) Sketch x = indieate the onientatiba of the 2t°, y = 3t, -4sts4 aud with %3D Curve an arow,

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Q: ston Compute the length of the circle of radius r defined parametrically by x = 3 cost, y = 3 sint ;…

A: given that x=3 cost , y=3 sint; 0≤t≤2π find out the length of the circle of radius r i.e. arc length…

Q: ..... The area of the surface generated by revolving the curve x = 1 cos (2t), y = 7+ -sin (2t) on…

A: Follow 2nd and 3rd step.

Q: Find the length of the circle of radius r defined parametrically by x=rcost, y=rsint,0≤t≤2π.

A: Here I am attaching image so that you understand each and every step.

Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

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Q: Verify Green's Theorem in the plane for F = -3y³i+ (3x3 + cos y)j where C is the circle x2 + y? =…

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Q: Use Green’s theorem to evaluate the line integral 2x2y dx + 6x3 dy, where C is the circle x2+y2 = 4,…

A: The answer is as follows:

Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

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Q: Find the surface of revolution of the curve y = 4 + 3x² that is rotated about the y- axis between 1…

A: We have to find the area of the surface of revolution of the curve y=4+3x2 that is rotated about the…

Q: Let C be the parametric curve defined by Ja(t)=1²-t-6, [y(t) = 41³ + 3t² - 6t. Determine the point/s…

A: a) Given that: xt=t2-t-6yt=4t3+3t2-6t For a horizontal tangent line, the slope must be 0. That…

Q: 3) Find the exact length of the curve. y = In(cos r), 0 < x<

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Q: c) By using Green's theorem evaluate $ (4xy – y°) dx + (x³ + 3xy) dy where C is a closed curve…

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Q: Use Green's Theorem to evaluate F. dr, C where F = (Va + 6y, 4x + /ỹ C consists of the arc of the…

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