Suppose that f(x, y) D [ f(x, y) dx dy X = - and the region D = [2,3] x [2,5]. Y =

Q: Calculate the line integral f -y²dx + xdy where ŕ is the path y² = 2x − x² such that x>1 and y > 0.

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Q: Suppose f(x, y, z)=x+y+z, h(x,y) = (x + y, x³, y) and g(x) = (x,x²). Calculate d =z=of oho g(x). dx

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Q: If S√√ƒ(² (b) If f(x, y) dA=0 then f(x, y) = 0 for every (x, y) in the region R.

A: (b) If  then  for every  in the region .To check: The correctness of the above statement.

Q: Suppose that f(x, y) = 2x + 2y and the region D is given by [-5, 4] x [-5, 4]. D [[ f(x, y) dx dy =

A: The given function is fx, y=2x+2y. The region D is given by -5, 4×-5, 4. We have to find ∬Dfx, ydx…

Q: Let f= 2zy + yx, v= [y, z, 4z -x]. Find Dyf at (2,1,2). NOTE: Enter an exact answer. Dvf (2, 1, 2) =

A: Given: fx, y, z=2zy+yx, v=y, z, 4z-xTo find: The directional derivative, Dvf at 2, 1, 2

Q: Suppose f(x, y) = xy² + 4. Compute the following values: f(4,-5)= ƒ(−5, 4)= f(0,0)= ƒ(5,-5)= f(t,…

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Q: Find an absolute extrema of f(x,y)=2x² - 4x + y² - 4y +1 on the closed triangular region bounded by…

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Q: 3. Find f 6y(x + 6) dà where D is the region bounded by x = - -y? and x = y - 6.

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Q: 2. Evaluate (x + y) dA, D is bounded by y = √æ and y = x².

A: The given integral is Where D is bounded by

Q: 3) Evaluate f.(y + z)dx + (x + z)dy + (x + y)dz, C consists of line segments from (0,0,0) to…

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Q: dy Given y = u? - 1 and x = u2 + 1, find dx

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Q: Suppose f(x, y) = xy² + 3. Determine each of the following: f(0, -2)= f(-2,0)= f(0,0)= f(-3,-2)=…

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Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: d₁: [x,y,z]= [0,2,1]+t[3,1,1] And d₂: [x,y,z]= [1,-3,0]+[2,-1,1]

A: If we have two points A(x1,y1,z1) and B(x2,y2,z2) then distance between A and B is…

Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y,z)= In (2³-4x³ - 3y³ - 2) 1…

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