270. f(x, y, z) = 1 √x² + y² + z², B = {(x, y, z) |x² + y² + z² ≤ 9, y ≥ 0, z ≥ 0} N 3 2 0 0 1 y 2 3-3 0 X 3

Q: Evaluate (x-5y+z)ds, where S - Sz 10 x, 0 ≤x≤ 10, 0y ≤ 10.

A: Step 1: Step 2:

Q: Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0<x < 2,0 sys 2, 0 s z < 1} .

A: We have to evaluate the triple integral given below: ∭B4z3+3y2+2xdV  Here, the region B in three…

Q: d²y 54. Let y = 4r+2r+l_find CL)

A: To find the double derivative of below expression.

Q: 3. x = 1-5t and y -t+ 3 for 2 < t<6 %3D y (x,y) Domain:

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Q: Given the vector field (yz, xz, xy) find a potential for this field.

A:

Q: 21. Let V1 = 1 0 -1 V2 H " V3 = 0 {V1, V2, V3} span R4? Why or why not? 1 0 0 . Does

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Q: c. P((X,Y) ¤ B3) where B3 = {(x, y) = R² : |x| ≤ 1, |y| ≤ 1}. d. P((X,Y) € B4) where B4 = {(x, y) =…

A: Given R={(x,y)Area of R=c.       Area of ,therefore     P((X,Y))==1d.   Area of ,therefore   P((X,Y)…

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

A: