Find the integral f(x,y,z)dA of the function f(x,y,z)=(x+2)(y+3)(z+4) over a right S triangle in the xy plane as indicated below. y 1 X 1

Q: Evaluate ʃC F dr where C is the parabola y = x2 from (0, 0) to (2, 4) and F (x, y) =< −ysinx,…

A: Given a curve C is a parabola from (0, 0) to (2, 4)

Q: Determine the expression for F(x, y, z) given the function F(x, y, z) = 2x²y = xz² + 3y²z.

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Q: - Integrate the function f orgy) =y-Vx over triangle cut from the first quadrant by Line X+y=1

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Q: Find the Zero and its oodex for the function flz)=1- Ti+Z+

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Q: Q.2 Find DivF and curlF at point (1,2) , where f(x, y) = xy² + Inxy

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Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

Q: Show that the function f(x, y) = x² + 2xy is differentiable at any point (zo, yo).

A: Given function fx,y=x2+2xy The sufficient condition for differentiability If a,b be a point of the…

Q: Find and sketch the domain of the function f(x,y) = cosx + V3x-y+2

A: The given function is .The objective is to find the domain of the function and sketch the domain.

Q: Determine the expression for Fyz(x, y, z) given the function F(x, y, z) = 2x²y – xz? 3y z.

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: Find the analytic function if the imaginary part is (2xy + 5y) where u (0,0) = 0

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Q: Evaluate (2x - y) dx + (x + 3y) dy. JC C: x-axis from (0, 0) to (0, -3) and (0, -3) to (9, -3)

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Q: luate Sa F . = 3x² i + (=

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Q: | (4z + 4y + 4+8zy) dA where R= [1,2] x (0,1]. R Let I Find

A: Given: ∬4x+4y+4+8xyddwhereR=1,2x0,11

Q: V4–x² – y² Let f(x,y) =- Shade the region in the x-y plane that corresponds to the domain of f(x,y)…

A: We are given the function f(x, y)=4-x2-y2lnx-y. For f(x, y) to be defined, we must have the domain…

Q: Evaluate SF-d F=(x² + y²)i-2xy j clockwise in the xy-plane x=0, x=4 and y=0,y=2. and C is the F-dr…

A: We know, for a force F→=P,Q, the line integral ∫CF. →dr→ is given by ∬(∂Q∂x-∂P∂y)dA, according to…

Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: X+Z+3Siny X +2y-2

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