Use Green’s theorem to evaluate ∮C(ye2xy−5y)dx+ (xe2xy−2x)dy, where Cis the counterclockwise oriented boundary curve of the square with vertices at(0,0), (0,1), (1,0), and (1.1).

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Q: 6. Parallelogram ABCD has its sides by AB = [5,2,3], and AD= [4,2,5]. Its fourth vertex is point C.…

A: We will use vector notation to find area first then calculate required side.

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Q: f (xy + yz + xz)dV, E E = {(x, y, z)|0 ≤ x ≤ 1, −x² ≤ y ≤ x²,0 ≤ z ≤ 1} 194. where

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Q: 45. Use the function fbelow to determine each limit: f(x): - A. lim f(x) x → B. lim f(x) x→-3- -2x…

A: The given function is f(x)=-2x/(x+3)2Find the limit. Find the right hand limit and left hand limit.

Q: Problem 8. rπ/3 Evaluate the iterated integral *** cos(x+y+z) dzdxdy. Answer:

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Q: Book Problem 5 Find the volume V of the solid formed by rotating the region inside the first…

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Q: Evaluate the double integral. 1/60-1² αA, D -y2 ¹ = {(x, y) | 0 ≤ y ≤ 4, 0 ≤ x ≤y}

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Q: V. Let R be the region bounded by the graphs of y=-x-1, y = 2³+1, the horizontal line y 3, and…

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Q: Find the Jacobian. a(x,y,z) = a(s,t,u) d(x,y,z) a(s,t,u)' where x = s - 3t+u,y=s+t − 5u, z = s + 3t…

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A: y" + y = csc xThis is the second order differential equation

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A: To Find :Antiderivative of

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Q: Determine a complete solution, y (x): use any applicable method   given: y'' - 4y = 4x - 3e^x

A: The given differential equation .We have to find the general solution for the differential equation.

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Q: 3. Find the tangential and normal components of the acceleration vector at the given point. (a) r(t)…

A: Find the tangential and normal components of the acceleration vector at the given point.

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Q: lim X118 9x-3 sinx √√49 + 49+16x2

A: we use some standard formula of limit

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Q: nd an antiderivative F(x) with F' (x) = ƒ (x) = 5 + 18x² + 14x6 ¬d F (1) = 0. emember to include a…

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Q: 4) Find the absolute minimum and maximum points of the function g(x, y) = x² - 2y² + 6y over the…

A: Here, the given function is Now

Q: State the range for the function f(x) = -In(x − 1) + 2 : O (-00,00) O (-∞, -1) O (0,00) O (-00, 0)

A: To find the range of the given function.f(x)= -ln(x-1)+2

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Q: lim x →∞ 7x-3 √√25x²-49

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Q: Evaluate the following integral. x=2 L. y=0 x=1 ry² dx dy= dy=| I dz)

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