2. Compute ¡ E x dV , where E “ tpx, y, zq | x ď 0, z ď 0, x2 ` y 2 ` z 2 ď 9u

Q: 16) Which function will shift y= vx right 4 units and up 1 unit? A) y = Vx + 4 +1 B) y = Vx + 1 C) y…

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Q: If f(x.y) = In(x² + y²) + find fr and fy -

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Q: Let f(x, y) = xy – y³ + x². where u =. O A. 37 O B. -37 10 37 √10 O D. -37 C. Du(f)(1,2)=?

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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: e /// 2 Evaluate 2xz dV where E {(x, y, z) |1 ≤ x ≤ 4, r ≤ y ≤ 2r, 0 <z<x+3y}

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: (18) Find [S], where S = {(a, b, c)|a, b, c E [100], a <b, a <c}.

A: Here is how the set S is defined: S = {(a, b, c) | a, b, c ∈ [100], a &lt; b, a &lt; c}   We must…

Q: 2. If F(x, y, z) = 2z3 – 3(x² + y²)z, then verify that Frx + Fyy + F2 = 0. %3D

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Q: dv av and ду ди ди 2. suppose f(z) = u(x,y) + iv(x, y), show that əx %3D ду əx ||

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Q: O Find Vf, where f(x, y, z) = = e¯(ax+by+cz) with a, b, c some constants.

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

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Q: 1) If f₁ ln x dx = 1 and ₁² lnx dx = 1+e² then fe² lnx dx = a) e² b) 2+ e² c) -e² d) −2+ e²

A: If ∫1eln x dx=1 and ∫1e2ln x dx=1+e2 then to determine the vaue of ∫ee2ln x dx.

Q: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: If f(z) = z² − (z)² + zz, calculate the following: a) u(x, y) and v (x, y) b) u(-10,-5) and…

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Q: 3 x dy + xy dx + x dy + 2ydx = 0

A: Given differential equations is first order variable separable differential equation.

Q: 4. Encontrar el area de la parte de la superficie y = 4x + z² que está entre los planos x = 0, x =…

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Q: 3zyz f(x, y, z) = e %3D fz fy = f =

A: The given function is f(x,y,z)=e-3xyz. Evaluate fx as follows. ' Thus, the value of fx is…

Q: Describe the domain of: Зху 3) f(x, y,z) = 4) f(x, y,z) = 1-x² – y² – z2 z- VX

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Q: SiSi dx dy dz Q4) Evaluate xyz

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Q: Let f(x.y) = In (x2y). If f,(2,1)=f,(5,a) what is the value of a? O a. -1 O b. 1 O.O Od.-2 O e. 2

A: For calculating the partial derivative we need to assume one variable as constant and differentiate…

Q: Which of the following expressions are not valid? Why? (a) [ f* 1(x, y) dy dz [T (c) [[1(x, y) dy de…

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Q: x-y x+y+1' 1. Let f(x, y) (a) f(2, 1) (b) f(1,2) (c) f(a, a) (d) f(y + 1,y) Find:

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Q: 1 x+R+ 2)²(x+ x+ R+ 4) dx (Hint: Let u= x+R+2 x+R+4

A: ∫1x+R+22x+R+42dx

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

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Q: dz If x4 – y4 + z - 3z = 2, then %3D %D dx a) 4x3-4y3 3-4z3 b) 4x3 3-4z3 c) None of these d) 4x3+4z3…

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Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

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Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: Find the values of af /ax and af lay at the point (4, 5) if f(x,y)=x² + 3xy + y -1

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Q: 3 For f(x,y) = In x+y°, 4,8)

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Q: Let g(x, y) = Vx²y². Find 1. g(1, 2) 2. g(4,1) 3. g(2, у) 4. g(x,2) 5. g(w, z – 1)

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Q: b) y = 1 - v 1 + v2 -82 dv dy = 1+v

A: