Let g) be a on .R Such thiat derivable ction g4)=5,914) = 2, t fin)=g(w) Coscn) egc) and f'ce).

Q: „Consider the space (R,T). where t={R,Ø}U{ACR:[0,1)CA} :Then (R,T) is not T, O T, but not T, O T2 O…

A:

Q: Use špheričal čoördiñatės. Evaluate tet dv, where E is the portion of the unit ball x2 + y² + z² s 1…

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: Let r(t) be a positively oriented rectangle with corners (0,0), (0,1), (2,1) and (2,0) and F(r, y)…

A:

Q: Evaluate ze dV, where E is the portion of the ball centered at the origin of radius 5, x + y+< 25…

A: Given Where E is portion of the ball centered at origin, radius 5 and lies in first octant. In…

Q: Use Divergence Theorem to evaluate ,0i +rj +ryh) ds, Q#3(a) where S is the upper part of the sphere…

A: As per bartleby instruction when more then one question is given only one has to be answered. Please…

Q: Show by Vector mothads that th ditonce hom fhe fornt P.(Xx, Y,, Z) to the plane Ax -+By+cz-D26 t of…

A:

Q: Find the area of the part of the plane  z = ax + by + c  that projects onto a region in the…

A:

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and %3D x? + y? + z? = 4 in…

A:

Q: Compute the distance d from y to the plane in R' spanned by u1 and uz.

A: We have to find the distance d from y to the plane in R^3.

Q: Assume s is a smooth surpace parametrized by e (u,v): <Jv, win' u, SZ-v ). Evaluatk 2x sin y do.

A:

Q: Use Green's Theorem to evaluate pxcosydx – ysinxdy, where the curve C is the square with 0), (TT,…

A:

Q: 18. Suppose that V ·F, = V • F, and V × F, = V × F, over a re- gion D enclosed by the oriented…

A:

Q: Compute the line integral ∫_C F · dr, where F (x, y) = 〈−x^3, xy〉 and C is part of circle x^2 + y^2…

A:

Q: 21. Show that the volume V of a region D in space enclosed by the oriented surface S with outward…

A:

Q: Consider the area of the part of the plane z=ax+by+c that projects onto some region D in the…

A:

Q: Evaluate the integral eiz dz, (22 + 1)2 where C is the circle |2 + il = oriented anticlockwise.

A:

Q: Let S be the torus parametrized by G(e,p) ((a bcos(p)) cos(0), (a +bcos(p)) sin(0), bsin(p)) for θ,…

A:

Q: Exercise 11. Compute the area of the pseudo-sphere, i.e. the surface of revolution obtained by…

A: Area= ∫2πrds=2π∫r.dr/sin(ϕ)∫2πrds=2π∫r.dr/sin(ϕ) Due to tangent property: r/sin(ϕ)=a,r/sin(ϕ)=a, and…

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: Use Gauss Divergence theorem to calculate (5zi+ 4yj- 2z k).n dA over the sphere S: 2 + y? + 22 = 9.

A: This is a problem related to vector calculus. Based on the general formula of gauss divergence…

Q: Use the Divergence Theorem to evaluate (5x + 10y + z) ds where S is the sphere x2 + y2 + z2 = 1.

A: In the given problem, S is the sphere x2+y2+z2=1Divergence Theorem:∬SF·n dS=∭Ediv F dVNow, the…

Q: Use the Divergence Theorem to evaluate (4x + 9y + z2) ds where S is the sphere x2 + y2 + z? = 1.

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Cannot solve

A: Multiplying and dividing first term by secx and second term by tanx of left hand side of equation ,…

Q: Find a conformal map that takes {z|0<argz <} onto the unit disk.

A: Given that a conformal map that takes z | 0&lt;argz&lt;π8 onto the unit disk.

Q: Are |z], Img(z) analytic? Give reason. sin Choose the suitable theorem to find the result of $ dz…

A:

Q: F. dS, where F(x, y, z) = z²xi + 2) + (x2z + y2)k and S is the top half of the sphere x² + y² + z? =…

A:

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = &lt;u,v,uv&gt; , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: Let F(z, y, 2) = 12?ri + (ty + tan(z))j + (1z?z+ 4y?)k. Use the Divergence Theorem to evaluate f, F…

A: We must apply the Divergence theorem on a closed solid, but the surface S is not closed (it is just…

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: Use the Divergence Theorem to evaluate (6x + 7y + z2) dS where S is the sphere x2 + y2 + z? = 1.

A:

Q: Identify the correct notation to transform rhombus PALE onto P"A"L"E" to show the figures are…

A: Geometry

Q: b. Describe the rigid motion(s) that would map AUVT onto ASVR.

A: Triangle SVR is congruent to triangle UVT by SAS congruence rule as per a. part. Four types of rigid…

Q: or tho gonal Use the least, me thad to find the squones projetiom of bz Ġ 2 -a anto the salwmin of…

A: Consider the given:         A=011211and  b=12-2T=12-2

Q: Prove that dr-V3Ta? where こis the intersection of the plates: x²+ and and F=ly,Z,x)

A:

Q: Consider 2-dimensional hyperbolic space with metric ds = dr'+dy and y > 0. The length of a line…

A:

Q: 3. Please give clear explanations

A: The parametrization of a surface S is given by       G(u, v)=(u, v, uv) where D is u2+v2≤1.

Q: Use a parametrization to find the flux F•n do of F = 5zk across the portion of the sphere

A:

Q: 13-Evaluate JSS zdV E where E lies between the spheres x2 + y? + z² = 1and x2 + y? + z? = 4 in the…

A: To find- Evaluate ∭Ez dV where E lies between the spheres x2 + y2 + z2 = 1 and x2 + y2 + z2 = 4 in…

Q: let s is the curved surface of the cylinder x²÷a² + y²÷b²=1 0≤z≤c , then evaluate…

A:

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

A: Solution :

Q: Let W = Span{u} where u -2. Let y = |1, find the distance from y to W L3]

A:

Q: Ex: © Suppise that the fuowing trausfruntiun Cowneciğa the (I') and (xi) coarduate رک سهاور؟ てス4ス)…

A: Given  x¯1=ex1+x2x¯2=ex1-x2 Required Jacobian is…

Q: #1. Find transfurmation that maps the strip o<y<l a on 2 -plane anto the disk ( WI<I on w-plane.

A: We have to find the conformal transformation function w = F(z), which will map the strip : 0 &lt;…

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: Evaluate the double integral / ydrdy where T is the triangle with vertices (0,-1), (0, 5), (4, 3).

A: First, draw the region of integration. Then, use the region to setup the double integral.

Q: Let F(x, y, z) = (x,y,z). Compute ∫∫sF · dS where S is the part of the plane x + y + z = 1 in the…

A:

Q: Evaluate / (7xi – zk) · ndA over the sphere S : x² + y² + z² = | S a) by divergence theorem, (b)…

A: a) By divergence theorem, ∬SA. ndA=∫∫∫V∇.A dV Now,  ∇.A=∂7x∂x+∂0∂y+∂-z∂z=7-1=6 By changing to…

Q: Use Green's Theorem to Calculate the Line Integral ſy²dx + x²dy, where c is the triangle o vertices…

A: Given that, the line integral is ∫y2dx+x2dy and the vertices of the triangle is 0,0,4,0 and 4,4. By…