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

Q: M. y dV, where E- {(x, y. 2) | 0 x* 3, 0 yx, - yEs+y}

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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: We know that S(x,y)dx + g(x,y)dy] = Se f(x,y)dx +Seg(x,y)dy. Use this knowledge to evaluate S.y dx+x…

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Q: iF w=f(x-y₁ y-Z, Z-x) then dw dw dw = ? dx dy dz Chain roll

A: Chain Rule : If w= f(a,b,c) and a=g(x,y,z) ; b= h(x,y,z) and c= l(x,y,z) then…

Q: Let f (x, y) = 2x3 + x2y - y2. Compute d2f/dx2, d2f/dy2, and d2f/dxdy at (x, y) = (1, 2).

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Q: We know that Sclf(x,y)dx +g(x, y)dy] = Sf(x, y)dx + S, g(x,y)dy. Use Sef(x,y)dx + S g(x, y)dy. Use…

A: We need to evaluate the integral ∫Cydx+xdy where C is the line segment from (1,-1) to (4,3).

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: Which of the following sets are linearly dependent in (-co, co)? S1 = (x, sin x, cos x} S2 = (sin…

A: We first find the Wronakian for each given set of functions and then evaluate the value of Wronakian…

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: S(x,y,z)= hn xyz +e (30) find f,, and f. 4

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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: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

A: We have to find ∫Cz-idz where C: γt=t2+1+it3, 0≤t≤1

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: 4. Use the linearization of f(x, y) Vx + 2y to approximate f(3.01,2

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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: Find the global extrema of f(x, y) = x3 - xy - y2 + y on the square [0, l] x [0, 1]

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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: 3. Use the transformation u = 4, v = xy to find || ry³ dA over the region R R in the first quadrant…

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

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Q: Given the line integral | (2x2° + 6y) da + (6x – 2yz) dy + (3a² z² – y²) dz. Let C be the path that…

A: Note that the following integral reduces like this :

Q: 14. We know that S(x,y)dx+g(x,y)dy] = Se f(x,y)dx + Se g(x, y)dy. Use this knowledge to evaluate S.y…

A: We integrate this by making two path where for one path only y vary and for other path only x vary.

Q: If f(x, y, z) = c²y² + ln(y+z), find ƒ₂(3,0,2), fy(1, 0, 2), and f(0,0,1)

A: We have to apply the partial differentiation to find solution of the given problem.

Q: 2. Find Df(x, y, z) for f(r, y, z) =x In z+r+ y at (0,0, 2).

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Q: Find SS, (x2 + y²)dA, where D is bounded by y? = 4x and y = x.

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Q: f(x, y) = 2x- xy + y, find (a.)and (b.) at (Xo, yo) didirectly from the definition. dx 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: 4. Evaluate ff(2x- y²)dA over the triangular region Renclosed between the lines y =-x+1, y=x+1, and…

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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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