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 (-1, –1) (1,–1) -2

Q: 5. Use Green's theorem to evaluate where C is shown below (6y - 9x) dy — (xy - x³)dx (-1,4) (-1,-1)…

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Q: if y= e-e-X dy %3D Show that %3D e* te*

A: We have to prove this equation

Q: 2) (1+ e*/y)dx + e*/y (1 – 2) dy = 0 Ans: x + ye*ly = c (Bali, 2007) %3D

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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: Example: » - ( ) F(r,y) = | x² + y² ' x² + y², on the curve C : R(t) = (cos t, sin t), t e [0, 27].…

A: Given : vector field F→x, y=-yx2+y2, xx2+y2 on the curve C : R→t=cos t, sin t , t∈0, 2π

Q: Compute Ay and dy for the given values of x and dx = Ax. y = x2 - 4x, x = 3, Ax = 0.5 Ay = dy Sketch…

A: In this question we have to find the value of △y and dy.

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: 3.) Calculate the curve integral f (1 – a² + y²) dx + (1 + x² – y°) dy. Here C consists of the…

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Q: Study the analytically of w = L(2) at the points z = 0, z= v2,z = -21

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Q: y = In(sec t), x = log(cosec t) In(sect), x %3D %3D

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Q: need help evaluating this quesion pls

A: Consider the given information:

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

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Q: 7. See the attached file dy 7-find for x?y2 = x2 + y? (use implicit differentiation) dy 2x 2xy? A)…

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Q: g(x), find dy by using Leibniz's notation for the chain rule: dx Give y = f(u) and u = dy dy du | dx…

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Q: Q1 Assuming that the equations in Exercises 25-26 define y as a differen- tiable function of x, use…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

A: Given: y=e2tsin2tx=e2tcos2t

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

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Q: dy in terms of t: Differentiate parametrically to find dx y= 2t2 +4 t - 1 X = A [4t(t – 1)²] В…

A: Given :x=1t-1y=2t2+4

Q: In Exercises 51 and 52, find dy/dx at the given point. 51. (x + 2)? – 6(2y+ 3)2 = 3, (1, –1)

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Q: Compute Ay and dy for the given values of x and dx = Ax. у- х2 - 4х, х - з, дх - 0.5 Ay = dy Sketch…

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Q: (b) Use a graphing utility to find dx/dt, dy/dt, and dy/dx at the given value of the parameter. dx…

A: Follow next step

Q: = Let {B(t), t≥ 0} be a standard Brownian motion and X(t) E [(X(2) + X(4))²]. -3t+2B(t). Find the

A: A Standard brownian motion is B(t) X(t)= -3t +2B(t) X(2)= -6+2B(2) X(4)= -12+2B(4) now we add X(2)…

Q: d In x Work out the following transformations (recall dx 1 ): dy d In x dy dy %3D dx dy -T² dT…

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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: In Exercises 53-56, find the equation for y, given the deriv and the indicated point on the curve.…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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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: dx dy. If y =x is expressed with parametric equations such that - 6when x=1, what is dt dt 12 -6 -12

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

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Q: 2. Let F(x,y) = (cos(x – 2y), –2 cos(x – 2y)). Find curves C and C2 so | that, F. dr = 0 F. dr = 1

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Q: (dy = arctan dx, (i) Use the facts: dy and (dy/dt) to find dt d dx (dx/dt) ds (ii) Use the fact that…

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Q: A point is moving along the graph of the function 1 y%3D 2x +5 such that dx/dt=2 centimeters per…

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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: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: dy for 2xy - 2x + 3y3 = - 42, with the conditions dt dx 3 - 12, х%3D3, у%3 Assume x and y are…

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Q: [&+2y)dx +(x² - 3y°)dy (3+2 4. Evaluate where C is any smooth curve from the point A (1, 0) to the…

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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: Scy dx –x dy; C is the cardioid r=1- cos 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: Assuming that the equations define y as a differentiablefunction of x, use Theorem 8 to find the…

A: Consider the given function, xy+y2-3x-3=0 now differentiate with respect to x,…

Q: Show that the graph of ř = (t sin t, t cos t, t²) lies on the paraboloid z = x? + y?.

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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: Example 1. Let f(x, y) = (y + 1)e²+v°, (a) Find the tangent plane to f at the point (0,0).

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

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Q: Let y = -. Find dy and Ay at x = 9 with dx = Ax = - 1. Enter the exact answers. dy = Ay =

A: Solve by using differentiation