Compute ffs FdS for F = < yz, ln(x +z), x² + z > where S surface of the olid region bounded on the "side" by the cylinder x² + y² = 1, on the top by the plane z = = 4, and on the bottom by the plane x + y + z = 1. Divergence neorem:

Q: The function G(x, y) G is defined by x² + 4y², if x² + 4y² ≤ 5 3, if x² + 4y² > 5. Show that G is…

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Q: Let F =   Find the outer flux of F through the surface S that is the portion of the paraboloid z =…

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Q: Calculate the outward flux F*n ds where F = (x^3, y^3) and C is the boundary of the region x^2 + y^2…

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A: If we look x varies from 0 to 2  y varies from 0 to 2

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Q: . Compute the line integral of E from B(0,0,0) to A(2,1,3) if E = -4xya, – (4y + 2x2)a, + 8zaz. Use…

A: The line integral of vector field E→ along curve C is ∫C   E→.dr=∫abE→(r→(t).r→'(t)dt  where r(t)→…

Q: Q2// A surface S is defined by x2 + z = 9 and the bounded by the planes y = 0, y = 1,x = 0,z = 0 in…

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Q: Q Find domain f (xry] and sketeh the region that represent thedomain -3 2 - のf (メッ) X -1 ニ 「メ+ッ?

A: To find the domain of the below functions. fx,y=x−ylnx−3 fx,y=x−1x2+y2

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A: The sketch of the solid region bounded is given below.

Q: Find the absolute extrema of f (x, y) = x^2 + y^2 + xy on the disk x^2 + y^2 ≤ 1.

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Q: Find the line integral of ​f(x,y,z)=x+y+z over the​ straight-line segment from ​(5,4,2) to (4,2,-2)

A: Note:- Since you asked multiple question ,according to our policy we can solve only first question…

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Q: 17. Given p(x,y,z) = xyz +5, find the surface integral of the normal component of grad o over x² +…

A: Given ϕx,y,z=xyz+5, We need to find surface integral grad ϕ over x2+y2+z2=9.

Q: Consider the function f(x,y) %— ху — х -4 у a) The critical point of f is (х,у)- (4,1) b) According…

A: Saddle point