NO Date Q:03 (0) Let V be a finite a dimenstonal ioner Product Prove Space over that R. Given uVE V - lu svll- lu- VR 4.

Q: OFind the V of He solid obtacred by rolating the ) Tle egun Under y x+2 [o,a] region aloout the…

A: Given:- y=x2 +2 , [0, 2] To find:- a. Volume of solid obtained by rotating region R about y axis  b.…

Q: Show that every positve colufion at Ay + B, k=osl,2 bounded, %3D JK is i-e, osysB-if A<1. 1-A

A: Question: Objective is to find the upper bound of     yk+1=Ayk+B, k=0,1,2,... where yk is positive.

Q: Let T be a triangle with the vertices (0,0), (1,0) and (1,2). Also, let V be the volume of the solid…

A:

Q: Let S be the solid bounded by the planes z = o and y + z = 3, and the cylinder x2+y2 =2y-

A: answer is in next step

Q: (a) Evaluate ([ Á.ds where A=(x+y²)î-2xj+2yzk and s is the surface of the plane in the first octant…

A: For the detailed solution of the problem follow the next steps.

Q: nclude spaces in between 5. d te In (In y)) at y dy

A:

Q: 2. If f e R[a, b], show using the properties of Riemann Integrability that there exists M > 0 such…

A:

Q: 1. Let d, be a metries on Xo and let the function a: X x XR defined be dr. y) dis. y)= prove that…

A:

Q: /Evaluate The are bounded by The Semiellipes y =2J5-x' oP The line 6 X = ±1 ,Y=-1 %3D

A:

Q: Verify the Divergence theorem over a cube in one unit on each side. The cube is situated in the…

A: By, Divergence theorem we have, The cartesian system for the first octant is,

Q: Find a transformation that maps the region S = {z = x + iy : x > 0 and –1< y< 1} onto the unit disk…

A: please see the next step for solution

Q: 1 : : Evaluate F dS whereF = (r",y",) and S is the solid bounded by the ry plane and the elliptic…

A:

Q: - The region bounded by y = 2 -x, y = 0, x = 1, x = 2 is rotated about the x axis. 197/12

A: volume generated by revolution of the solid is 19π12 detailed solution with explanation is given…

Q: Verify the Divergonce Theorem for F=(2x-x)+x*y} -aż? taken over the bounded by x -o, X=1, y=0,…

A:

Q: Let I = , zdV ,where D is bounded by the planes x = 0, z = 0, x+ y = 2 and the cylinder x2 + z2 = 1…

A:

Q: 4. Show that the line integral of F = [0, z] around a closed curve in the r- y plane, oriented as in…

A:

Q: 2.8 Using the divergence theorem, show that the volume, V, enclosed by the surface I can be obtained…

A: As per the Gauss Divergence Theorem, the surface integral of the normal component of G vector…

Q: 2. Let W be the union of the first and third quadrants in the xy- plane. That is, let W = xy 0 a. If…

A: According to our company gardening can answer only one question. If a specific questions are asked…

Q: * Use the Grom Schmidt process for thi two_ dmensional space: 2 3. 4 2

A: Gram Schmidt process is given by: uk→=vk→−∑j=1k−1uj→⋅vk→|uj→|uj→   v1→=201, v2→=3-51, v3→=042,…

Q: Consider the region between f(x) = /ĩ and the x-axis on [0, 4]. For each line of rotation given in…

A: The function given to us is  f(x)=x

Q: Use Green's Theorem to evaluatc the integral x²ydx + xydy where C is the rectangle with vertices (0,…

A:

Q: 3. Find the circulation of F 2xi + 2zj +2yk around closed contour %3D

A:

Q: å:RR→R be defined by dcx.y)=|xl+1yl, HxixR (R,d)is Than a metric space.

A: As per our guidelines we supposed to solve the very first question when the multiple questions are…

Q: Evaluate. where G is a solid that lies in the first octant bounded by x^2 + y^2 = 3z and z = 3.

A:

Q: Verify the divergence theorem for F= 3i+xyj+xk taken over the region bounded by z = 4-y^2 , x=0 and…

A:

Q: Q5. Analyze and Verify Gauss divergence theorem for F 2 xz i+ yzj+ z? k over the upper half of the…

A: Here, F=2xzi+yzj+z2k Given upper half of the sphere x2+y2+z2=a2. Let ∅=x2+y2+z2-a2=0…

Q: Evaluate || F-n dS where S is the cylinder (including the disk on the bottom) x² + y² =1 for 0<z<1…

A: First, we plot the given surfaces.Cylinder : x2+y2=1; 0≤z≤1Paraboloid : 3x2+3y2+z = 4; 1≤z≤4.

Q: Describe the 1-point compactification of (1) open ball in R3. (ii) (0, 1) x (iii) (0, 1) × S' (0, 1)

A:

Q: Again let F =. Find the circulation F. dr, where C is the boundary, taken 0 sys 6-2x. (Hint: Green's…

A:

Q: Evaluate the circulation of G = ryi + zj + 2yk around a square of side 7. centered at the origin,…

A: Given  G=xyi+zj+2yk around a square of side 7

Q: Evaluate the double integral I2 = || y'dzdy T where T is a triangle with vertices (-4, 0), (0, 1),…

A:

Q: 4. Verify Divergence Theorem for F =x?i + zj + yzk, taken over the cube bounded by x= 0, x = 1, y =…

A: Gauss divergence Theorem.  Let v be volume bounded a closed surface S and F be a vector…

Q: I have trouble getting to the answer. Just wondering if I can get it step by step.

A: Consider the region for solid.Let the solid be bounded by the coordinate planes and the plane 2x +…

Q: 8. Evaluate the double integral // ydrdy where T is the triangle with vertices (0,-1), (0,5), (4,…

A:

Q: Verify the Divergence Theorem: ls F- dS where F= (3z + z",y – sin zz, 2z+ ye) and Sis surface of box…

A: We need to find integral using divergence theorem.

Q: d. Dse the bosic properhes of integrC followng theorem. THEOREH:If (Cx. Y) = FG)G(), wbe La,bland G…

A: We will use dominated convergence theorem to prove the given theorem.

Q: Evaluate the circulation of Gayi + zj+5yk around a square of side 9, centered at the origin, lying…

A: Solution :

Q: 53. Verify the divergence theorem for A = 2x?y i – y² j + 4xz2 k taken over the region in the first…

A: Given : A=2x2y i- y2j + 4xz2 kbounded by y2+z2=9 and x=2

Q: Evaluate both sides of divergence theorem for A = pa,+ pcos(ø)a,+ zaz through the closed surface…

A:

Q: A solid G is bounded by the paraboloid z = 4 – r - y², the cylinder 2+ y = 4 and the plane z = 5.…

A:

Q: evaluate both sides of divergence theorem for A= ra,+rcos(8)a , +r²a, through the closed surface…

A: Given problem is :

Q: Verify Divergence theorem for the function F = e,p over the semi-cylindrical volume { x* +y° sa…

A:

Q: Let S be the sphere of radius 2, oriented inward. Let F = (2x + e", 4y + e*, 2:2). Use the…

A: In the given question we have to solve the double integral s.t∫∫F.ds  to the help of divergence…

Q: 4. Use the Divergence Theorem to evaluate the flux integral JS, F-ndA over the surface of a…

A: Given that, F=(3xy3z5,3y,-xy3z6)F⇀=3xy3z5i^+3yj^-xy3z6k^ We have to evaluate the integral  ∫∫sF⇀.ndA…

Q: $ ((x,y) (E,6) )e product Prove 2 xt + 3yt on e?. Gompute inner IL(,2), where the norm i's…

A: We have to prove that f( (x, y) , (t, t) ) = 2xt + 3yt is an inner product on R2 . 1.) &lt; ( 0, 0 )…

Q: (z+1)dz Evaluate using Cauchy's Integrati on Fromula where Cis z+2| z'4z

A:

Q: (a) Using the divergence theorem show that F.n ds = 0, where F(x, y) = yi-aj and D is a unit disc.…

A:

Q: Use the Divergence Theorem to evaluate the flux of the field F(x, y, z) = (e,3y+ sin (x'z), 8z + Vx2…

A: Given: Fx,y,z=ez2,3y+sinx2z,8z+x2+9y2 The surface S is bounded by the paraboloids x2+y2=z and…

Q: "roblem #5: Use the divergence theorem to find the outward flux F.n dS of the vector field F =…

A: