Use the Divergence Theorem to evaluate each of the following: (a) |/ ((2x+ yz)i – 2yj + (z² + x)k) · ndS, where S is the sphere z? + y? + z2 outward (positive) orientation. = 4 with (b) H.e (zzi + 2yj + 4e*k) - n dS, where S is the surface of the rectangular solid bounded by I = 0, y = 0, z = 0, r= 1, y = 2, z = 3 with outward (positive) orientation.

Q: 5. Find a parametric representation for the part of the sphere x + y + z2 = 4 that lies between the…

A:

Q: Find the surface area of the portion of the part of the paraboloid z = 7 - 2x² – 2y² that lies above…

A:

Q: 12. Find the area of the surface generated by rotating the curve y = √√x the y-axis. Do not…

A:

Q: Write the sphere equationil odi lo anoitaupo ontemeeg bas Totoov bnif (d) x2 + y? + z2 + 2x - 4y –…

A:

Q: Find the surface area of the portion of the plane z=6-3x-3y which lies in the 1st octant I)2sqrt18…

A:

Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: Find the "Area" of the "Surface" The part of the paraboloid (x y² + z²) that lies within the…

A:

Q: Evaluate /| cos(x? + y²) dA, where D is the D disk x? + y <I Select one: a. -n O b. A O c. O O d. 2…

A:

Q: Evaluate (image) over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 }

A: Given integral is ∭x2+y2+z2xyzdxdydz over the sphere D = { (x,y,z) | x2 + y2+z2 ≤ R2 } Change…

Q: ∫∫sy2 dS where S is the part of the sphere x2 + y2 + z2 = 1 that lies above the cone with equation z…

A: ∫∫sy2 dS where S is the part of the sphere x2 + y2 + z2 = 1 that lies above the cone with equation z…

Q: D) Evaluate f (r² + y²) dady where D is the disk z² + y² ≤ 4. Usc polar coordinates. (Ans: 647/5) E)…

A: To solve the following

Q: Use the Divergence Theorem to evaluate J where S is the sphere x² + y² + z² = 1. (11x + 9y + z²) dS

A:

Q: Exercise 1.6.101: Let x' = (x - 1)(x - 2)x². a) Sketch the phase diagram and find critical b)…

A:

Q: 4. a) Find the point on the unit sphere x² + y² + z² = 1 that is closest to (1,2,3). b) Find the…

A:

Q: JJs where S is the sphere x² + y2 + z2 = 1.

A: Given S is the sphere                         x2+y2+z2=1 To evaluate:             ∫∫S3x+3y+z2dS…

Q: 1. Find a parametric representation for the surface: the part of the sphere x2 + y? + z2 = 4 that…

A: According to the given information, It is required to calculate the parametric representation for…