Convert the double integral [[ (x + y)ex²-y² dA to uv-plane where R is the rectangle enclosed by the lines x - y = 0, x − y = 2, x + y = 0 and x + y = 3, using the change of variables x = -— (u + v). y = -— (u – v).

Q: Evaluate the line integral [[(3.ry² + 6y) dr, where C' is the path traced by first moving from the…

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Q: 5. Find an equation plane to the surface (u, v) = (3 cos(u) sin(v), 2 sin(u) sin(v), cos(u)) at the…

A: First, we find the point on the surface where the tangent plane would be drawn. Next, we calculate…

Q: Evaluate L₂Lova (4-3²) dydx -√4-x² by using polar coordinates.

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Q: B- Find the directional derivative of the function W = x² + xy + z³ at the point P: (2,1,1) in the…

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Q: Describe the image of the line z = 1 + iy under the map flz) = sin z %3D

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: 1 (x+y')* dy dx -J3X 2

A: Double integration of function gives the area under the function curve. Double integration can be…

Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: X- An ant is moving on the surface z = x² + xy + y² such that its - and y-coordinates satisfy cost,…

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Q: Find polar coordinates (r,θ) where r < 0 and 0≤θ≤2π of(√3,−1)

A: Given point in the rectangular coordinates is 3,-1. To find the polar coordinates r,θ, where r&lt;0…

Q: n exact form. Use symbolic notation and fractions where needed.)

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Q: Evaluate where F(x, y) = x² i+(y² – x) j and C is the line segment from (2, 4) to (0, 4) followed by…

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Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

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

Q: 5. Let L₁ be the line with parametric form (x, y, z) = (1, 0, 2) + (-1,2,3), and let L₂ be the line…

A: Given,The parametric form of the line ,The parametric form of the line ,.Aim: (a) To find the angle…

Q: Find domain and vange f (2y)- し、 (x'+ゴ) ) fCz, y) = Sin" (y-z) Ž (3,y)- tan

A: According to the question,  We need to specify the domain and range of the given function: (A) f(x,…

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Find the tangent plane to the equation z = 6y cos(4x – 2y) at the point (2,4,24) Z =

A: It is given that z=6ycos4x-2y and the point is 2,4,24. Recall the fact that if the equation of the…

Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: Consider the function f(r, y) = e=² sin( q² + y²) (a) ) Compute the gradient of f. (b) 1 ) Find the…

A: Given fx,y=e-xsinx2+y2

Q: Find the directional derivative of f (x, y, z) = 2z²x + y° at the point (2, 1, 2) in the direction…

A: Here, f(x, y, z) is given we have to find directional derivative of f(x, y, z) at point (2, 1,2) in…

Q: 6. Let F(x, y, z)=2xy² + 2yz² + 2x²z. a. Determine the maximum directional derivative of F at the…

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Q: l+vI+r² xy dydx -z 1-VT-

A: ∫01∫1-1-x21+1+x2xydydxTo transform to polar coordinates and calculate