Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

Q: Use Green's Theorem to find f. [(2x – y+ 4) dx + (5y+ 3x – 6) dy] around a triangle in the xy plane…

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Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

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Q: 6. Use Green's Theorem to evaluate (y- ry') dr + (2- r) dy where C'is shown below. x +y =

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Q: Which of the following is dy for the curve dx defined by x° – y³ = 2xy? 3x2-2y а. 2x+3y2 3x2-2y b.…

A: Find the derivative of the given curve and match with the correct option.

Q: In Exercises 55 and 56, find both dy/dx (treating y as a differentiable function of x) and dx/dy…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Suppose the closed curve C in R? starts at the point (-1,1), goes along the parabola y = x2 to the…

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Q: Let C be a portion of a curve from (2,0) to (2,2). Let F(r,y) = (tan(x²) + e²v¸ 2re²v

A: Introduction: A vector field is conservative if ∂P∂y=∂Q∂x, Where f(x,y)=Pi+Qj.

Q: An object is moving along a path defined by the graph  x^2+y^2=18 Compute  dy/dy, if dx/dt=-2,…

A: According to the question:

Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

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Q: Which of the following gives the length of the curve y = Vx over the closed interval [1,4]? (A) - dx…

A: Explanation and solutions is given below....

Q: 3. Use Green's Theorem to evaluate J(* -6y)dx+(y +10y)dy where C is shown below.

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Q: Compute dy/dx and d^2y/dx^2 for the following parametric functions

A: Given: y=e2tsin2tx=e2tcos2t

Q: Q4. Let C be a portion of a curve from (2,0) to (2, 2). Let F(r, y) = (tan(2²) + e²", 2.re²y + cos…

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Q: Evaluate d:/dx on the surface x: + + x²y®=² = 3 at the point (1, 1, 1).

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Q: An object is moving along a path defined by the graph x + y = 29 Compute dy/dy, if dæ/dt = 3, x = 2,…

A: Given the function f(x, y) :

Q: 4. Let f(z) = 1 23 1 - and find [ f(z) dz, where C a circle of radius 2 about the origin with…

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Q: Find the work done by F in moving a particle once counterclockwise around the given curve. F= (4x-…

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Q: 4. Use Green's Theorem to evaluate | xy dx + (1 – xy°) dy where C is shown C below. y (1,4) (-1,2)…

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Q: Use Green's Theorem to evaluate the line integral √(x - (y - x)dx + (2x - y)dy for the given path.…

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Q: Q.3 a) Verify Green's theorem for |(x2 + 2xy) dx + (y? + x³y) dy Where c is a square with vertices…

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Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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Q: Evaluate x*dx C + xy dy, where C is the triangular curve consisting of the line segments from (0, 0)…

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Q: Consider the closed curve in the xy-plane given by x² + 2x + y* + 4y = 5. dy -(x+1) (a) Show that dx…

A: Given data:   The expression for the given function is x2+2x+y4+4y=5.   (a) Differentiate the above…

Q: Draw direction field of the DEQ below, by hand, and sketch an approximate solution curve that passes…

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Q: Evaluate S. (2xy – x²)dx + (x + y²) dy such that c is a curve bounded by y? – x , y – x² ?

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Q: Use Green's Theorem to calculate 4. [(x² – xy) dx + (y² - 2xy) dy] where C is a square with vertices…

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Q: The area enclosed between the curves p(a) =2 +*+ 3 and g(@) = -22 - * + is O 16 47 %3D 18 49 O -49…

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Q: 2л where a, b > 0. dx = - ile* + b Prove that %3D

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Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Given:           x3−2y2+xy=0,     (1,1)

Q: 1. Use a change of variables to evaluate || ソーx dA where R is the trapezoid with vertices (1,0,…

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Q: Use Green's theorem to evaluate S,(5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: Der. 2D 11 Find dy/dx and d2y/dx2. For which values of is the curve concave upward?

A: Given: x=t2+1 y=t2+t Differentiating x with respect to t, dxdt=2t Differentiating y with respect…

Q: Find the aera under the curve y = cosx fx sec²(ax² )dx a #0 Form x = 0 to x = 7/

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Q: Use Green's Theorem to evaluate Se xy dx + (1 – æy³) dy where C is shown below y (1,4) (-1,2) 2 1…

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Q: S, (x + 2y) dx + x dy. C consists of line segments from (0. 0) to (2. 1) and from (2, 1) to (3, 0)

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: Show that the line integral / 2re" dx + (2y – x²e¯") dy is independent of path where C is any path -…

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Q: Use Green's theorem to evaluate (2y dx - x dy) around the closed curve C. y (2,5) 4 3 2 C 1. -2 -1…

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Q: 2. If F(x, y, z) = y²i+(2xy+e3=)j+3ye³=k. Evaluate F·Î ds, where C is the curve represented by r(t)…

A: Given F→x,y,z=y2i^+2xy+e3zj^+3ye3zk^ and the curve is C given by r^t=cost,t,sint,  0≤t≤π2. Find…

Q: Use Green's Theorem to evaluate x' dx + xy dy where C is the triangle with vertices (0,0), (1,4),…

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Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

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Q: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: the equation we have  (x3-y4)6+ln(x2+y)=1

Q: Use Green's theorem to evaluate f (x²y) dx + y²dy here C is close path formed y = x and y = x³ from…

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Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

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Q: Use Green's theorem to evaluate S. (5xy + x² + y²) dx + (x² – y)dy where C is a closed curve that is…

A: According to the given information, it is required to use green’s theorem to evaluate the integral.

Q: Evaluate [xy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4). [Verify using Mathematica]

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