af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

Q: 1.n f csc n? de y2 - 2y + 3 2.5; Vy - 3y: + 9y – 21 dy

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Q: along the following paths C:(a) x=2t^2, y=t, z=t^3 from t=0 to t=1; (b) the straight lines that A ·…

A: We will use parameterization to find line integral

Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: If R = {(r,y): (x- 1)2 + y² 0}, then 6y dA a. 5 O b. 8. d. 9. 2. 1.

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Q: 1. Find 2(3z + 4)² dz.

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Q: EVALUATE Sx csc(2x) cot(2x) dx A. -z csc (2r) +in esc (2r) - cot (2-)| + C В. B. z csc (2z) + In…

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Q: 6. Find (x + 3y)dA where D = {(x, y) | æ² + y 0}

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Q: -dx. (3x² + 1)ª Evaluate -1 +C OA. 18(3x² + 1)³ O B, In(3x2 + 1)ª) +C 1 OC. + C 18(3x² + 1)³ x2 +C…

A: Given- ∫x3x2+14 To find- The value of the integral

Q: Find fy (-1,-4,-2) if f(x, y, z) = x³ z4 + 2xy – y? z + 1.

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Q: Given f(x, y) 90x + 80y - 2 – 4y? – xy, and evaluate f(8, 5). f(8, 5) = %3D

A: Given : fx , y = 90x + 80y - 2x2 - 4y2 - xy  To fine : f8 , 5 Solution : For value of fx , y , put x…

Q: Y = -2X, then p(X, Y) = 1?

A: Solution

Q: Find f f(x,y) dA, where f(x, y) = x and R = [5, 10] × [-5, –4]. SSR f(x, y) dA=

A: The given function is f(x,y)=x, and the domain is x,y∈5,10×-5,-4. To Evaluate: ∬Rf(x,y)dA.

Q: If fxy (x, y) = y for 0 2X - 2) =

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Q: 15 -8 -3

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Q: Find V · (V x F), if F(x, y, z) = 5e*?i+ 9xe"j – 6e²k. V · (V × F) =

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Q: Graph the quadric surface given by y = √x² + 4z². Carefully explain your graph by identifying the…

A: The objective is to graph the quadratic surface.

Q: xy? Zy if z = 3x – 2y

A: Finding the partial derivative of z with respect to y

Q: If feF - dr = Sc(4x + 4y²) dx + (x²y) dy, what is.

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Q: If 2x = xy + y2, then A. C. -2 + y x + 2y (2-y) x + 2y dx 11 B. D. -(2 + y) x + 2y -(-2+ y) x + 2xy

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Q: Find // (5x + y)dA where D : {(x, y) | x² + y? 0}

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Q: Find df (3x + 2y)dA where D = {(x, y) | x² + y² ≤ 25, x ≥ 0} 500 3 X

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Q: dy If y=Vx+1, then is dr 1 A B) x+1 3 x(x²+1) 2 1 D 3 (x²+1) 2

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Q: 1-y Q2: Evaluate fo y²(x² + y²)dx dy -1

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Q: ind V. (V × F), if F(x, y, z) = = V. (V X F) = ezi+ 6xe¹j - 3ek.

A: Topic:- vector algebra

Q: dy t 3xy=xy?, y(0)= -3

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Q: dy is If x? +2xy= y2, then dx A 2x+2y X-y B 2(x + 1) X +1 + |>

A: Given: x2+2xy=y2 The objective is to find dydx

Q: Given y x+1 =25, is dx 2y A) x+1 2y B x +1 y (c) 2(x + 1) y D 2(x + 1)

A: Given that yx+1 =25  we have to find the value dydx. To find the derivative we use product rule of…