Given F(x, y, z) = (z, x, y) Solve for: а) divF b) curlF

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: Given: z = a' + æy", r = uv² + w®, y = u + ve" az Find when u = 2, v = – 3, w = 0 dv

A:

Q: f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball x² + y² + z² 2.5

A: Here we will use cylindrical co ordinate system to find value of integral  By using above figure…

Q: Find the average value of f(x, y) over the plane region R.

A:

Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

A:

Q: Given: z = x3 + xy", æ = uv + w°, y = u + ve" az when u = 3, v = – 2, w = 0 Find

A:

Q: "en J(2, 9) 5y), find =(z, y) = (z, y) = -(z, y) = %3D

A: We wil find the second order partial derivative.

Q: // | *dædydzB = {(x, y, 2) =€ R® 0 <« < 1,0 < y < 1,0 < z < x} {(x, y, 2) =€ R° 0<æ < 1,0 < y < 1,0…

A:

Q: Given w = xysin(z²), x= s-t, y = s², z= t². Find ay

A: Explanation of the answer is as follows

Q: The value of the line integral S(2xy dx + 2x?ydy + dz) C along a path joining the origin and the…

A: We have to find the value of given line integral.

Q: Among all rectangular boxes defined by the inequalities 0 ≤x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1, find the one…

A:

Q: Evaluate //. dV, where E x2 + y² + lines between the spheres x + y + z? and x + y? + z2 = 25 in the…

A: Consider the provided question, Evaluate ∫∫∫E1x2+y2+z2dVwhere, E lines between the sphere x2+y2+z2=1…

Q: Find the area of the surface. The part of the paraboloid r(u, v) = ucosvi+usinvj+u*k; 0<us3,0svS2n 5…

A: Area of the surface is given by:          A=∬ru×rvdudv

Q: 2 Evaluate [I, (x² +y² +z? dv, 2 В

A:

Q: 4. The square STUV has diagonals that intersect at point W, where SU = 4x + 26 and TW = 8x- 41. Find…

A:

Q: Find Duf at P. f(x, y, z) = 4x'y°z?; P(1, – 2, 1); u = - 2. Duf

A: The objective of the question is evaluate the directional derivative at a given point.

Q: Among all rectangular solids defined by the inequalities 0≤x≤a, 0≤y≤ b, 0≤z≤ 1, find the one for…

A:

Q: find the value(s) of a making v⃗ =7ai⃗ −3j⃗ parallel to w⃗ =a2i⃗ +6j

A: We have to find the values of a

Q: Evaluate // e² dV where E is enclosed by the paraboloid z = 2 + x² + y², the cylinder E x² + y? = 3,…

A: Since we are given with the multiple number of questions and answered according to the guideline.

Q: if x? + y? = 4 then prove that = d'y dx %3D

A:

Q: What is the dimension of {(x, y, z) E R³ : x +y+z = 0}?

A:

Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

A:

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: (a) Vx E R, 3y E Z such that y > x + 110. (b) Vx E Z, 3y E N such that y > x + 110. (c) 3x E Z such…

A:

Q: a) If W =(x,y), where x v²-g' and y 2vg calculate W+ %3D

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Given f(r, y, z) = – 5e 4ayz, find %3D fr(x, y, z) = f,(x, y, z) = f:(2, y, z) =

A:

Q: Given: z = = x* + zy°, * = ww* + w, y = u +ve" a z Find when u = - 3, v = 2, w =

A: Given: z=x4+xy3x=uv4+w4y=u+vew The objective is to find ∂z∂u, when u=-3, v=2, w=0

Q: Given: y2, = uv4 + w*, y = u + ve"| z Find when u 1, v = 3, w = 0

A: We know:

Q: (b) Let h(x, y, z) = x?y+ yz?, where a = u + v, y = u – v and z = -u. Calculate and ди dv

A:

Q: Evaluate fff(x +y +:' dV, where a is the solid hemisphere (half of the sphere) enclosed by x +y+ =1…

A: Here in the given question, find the integration of the given function:∭Dx2+y2+z232dVWhere Ω is the…

Q: 2² dædydzB = {(æ, y, z) =E R° 0 < æ < 1,0 < y < 1,0 < : < x}

A: Given triple integral  ∭Bx2dxdydz, where B=x,y,z∈R3:0≤x≤1,0≤y≤1,0≤z≤x. We have to evaluate…

Q: Find Duf at P. f(x, y, z) = 6x°y°z*; P(1, – 2, 1); u = i %3D Duf = i

A:

Q: Evaluate cz dz, where c is |z| = 1 zG-2) Inz %3D

A: Let

Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

A:

Q: Evaluate /// xe²+y²+z² dV, where E is the portion of the unit ball x2 + y? + z2 < 1 hat lies in the…

A: Given The given integral is ∫∫∫Exex2+y2+z2dV E is the portion of unit ball x2+y2+z2≤1.

Q: a(x, y) r = u? -v,y =ue". Compute ô(v,u)

A:

Q: If z = f(x, y), where x = 2ts and y = t2 + s², show that () - 2 + 2x + 4y %3D dsdt

A: Here given z=fx, y and x=2st, y=s2+t2

Q: Solve the IVP y" + 4y/ + 5y = 38,(t), y(0) = 0, y'(0) = 1. %3D %3D

A:

Q: Given f(x, y, z) = 4x2 + 2y? + 6z?, find %3D fa(x, y, z) = fy(x, y, z) = f:(x, y, z) =

A: To find fx(x,  y,  z) =........... fy(x,  y,  z) = ...........  fz(x,  y,  z) =............

Q: Given f(x, y, z) = V5x – 5y + 2z, find fa(x, y, z) =| %3D fy(x, y, z) = f-(x, y, z) =|

A:

Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

A:

Q: Solve the fAllowing equetiun by cepuration of warnoble methal xQu-y Du t Zy = X Y glven uli,1)= 3…

A:

Q: dv E={my,)|→<y<4Y<そく4, Osns? そ

A: Given that  Triple integral of z/(x^2+z^2) To evaluate the integral

Q: f(z, y) – zsiny +e, then Vf(r, y) (0, e").

A:

Q: Evaluate +y² 1 Ez² + y² JJJ₁² dV, where E lies between the spheres z² + y² + 2² +2² 16 in the first…

A: Given that,

Q: (b) xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z < 0}.

A: We have to evaluate given integral:

Q: If f(2) = sin(z?) = U(x, y) + iV (x, y), determine U and V. Verify that the C-R

A:

Q: Given: z = a? + xy*, x = uv² + w*, y = u + ve" dz Find when u = - 2, v = 1, w = 0 du

A: