Suppose = (4, –4, 1) and i = (3, 1, –4). Then ux v is and ひ×u is

Q: f(æ, y, z) = æ²y+ 2y²z+ 3æz?. Compute fa: (1, 1, 1). None of these. 3

A:

Q: If f(x,y) = x In(2y³ – 5) + y e* , find ! of and ôx ây

A:

Q: (b) If V'u =0 for x2 0 and if u f(y) on x=0, Show that ,y): +(y-5)

A:

Q: if w= fcu) and メ show that U ニ メャy? X Jw うx ニ0

A: We have given;

Q: Given F(r, s, t) = r(3s4 – 6t°), compute: Frst

A: This is a partial differential problem

Q: If u * v = 2i - 3j + k, what is v * u?

A: As we know a×b = - b×a

Q: dz If z(x, y) = x²y, æ = 4, and y = u³ v², find du

A:

Q: If u = 5i + 2j, v = i - j, and w = 3i - 7j, find u . (v + w).

A: According to the question, we have to find the value u·v+w, if u=5i+2j,v=i-j and w=3i-7j. The above…

Q: If (x, y) = (-V3, 1) , then find r and 0.

A:

Q: 1. If 4=x'zi-2y'?'j+xy'zk , find div4 at points (1, -1,1).

A:

Q: Suppose E(X) = 2, V(X) = 4, E(Y) = 6, V (Y) = 8, and E(XY)= 10. (1) E(X +Y) (2) V(2X +3Y) (3) V (2X…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: If u = (1,0), then Düfz(-3, 4) = ƒxy(−3, 4). True False

A:

Q: Let X ~ NB(r, p). Find M,(1). а. Use M,(t) to find E(X). Use M, (t) to find V(X). с. b.

A:

Q: If u = eª₁x+₂y+a, where a₁, a2, a3 are constants and 2² u J² u 2² u + = U. a² + a² + a² = 1. Show…

A:

Q: Given F(r, s, t) =r(3s² + 9t°), compute: Frst

A:

Q: Use Cramer's ru;e to fins a solution: 5x+4y=12 3x-6y=24

A: System of equations are 5x+4y=123x-6y=24

Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf (2,-1, 1) = =, then %3D A) B) 11 C) D) E)

A: The function is given by fx, y, z = ln2+x2-2y2-3z The vector is given by u→ = 1, 1, -1 To evaluate:…

Q: If S 3D [x|0 <x<12}, М 3 [x| 1 <х < 9}, and N %3D (x | О <x< 5}, find а. MuN b. M N N c. M' N N'

A:

Q: If z = xye», x = u · 3“, and y = u · v², find dz when u ди 2 and v = 5.

A:

Q: If u = (u, uz) and v = (V1, V2), how do you find u + v?

A: Given: u=(u1,u2)v=(v1,v2)

Q: (b) If z =W, show that: x- y xy 0 =

A:

Q: Show that A Yk= V' Yk+r

A:

Q: Given F(r, s, t) = r(3s² + 3t²), compute: Frst

A: Solution of question is written in below steps.

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 2x − u + 3v + w = 0

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

Q: If a > 0 and [[ 20*+v 20+u° dr dy = 1(e* – 1) , a =?

A: Using polar coordinate evaluate the above integral

Q: let R = (-2, 7). Calculate the following: The components of u = PŔ, where P = (1, 2)

A: Given,               R=(-2, 7)   and   P= (1, 2).    The components  of u=PR⇀=?

Q: 3-VE For dz, z = 2+vz

A: Given,             ∫3-z2+zdz

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: If u = ₁+₂y+z, where a₁, A2, A3 al constants and J²u J²u J²u น a +a+a = 1. Show that + + = U. მ2 მყ2…

A: This question is based on Partial diffrentiation.

Q: Find and d?z and prove that 2 0²z IF 2 = f(xt ay) + F CX-ay) %3D

A:

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: If z = (2x + 3y)³ and x = r2 - 2s and y = 2s - r, then when r = 2 and s = 1 is as %3D %3D

A: To find the partial derivative when r=2, s=1.

Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

A:

Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: If A = 2.x2i – 3yzj+xz²k and o = 2z – x°y, find A.Vø at the point (1, –1, 1). |

A: The gradient is calculated using the del operator and it can be represented as ∇=∂∂xi^+∂∂yj^+∂∂zk^.…

Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

A:

Q: xy Let z . Then: 4x2 – 5y? | az dz ду

A:

Q: . If 4=(x+2y+az, bx-3y-z,4x+cy+22) is irrotational. Find constant a,b,

A: Follow the procedure given below.

Q: 3. If (x, y, z) = xy²z find grad 6 at (2,−1,3).

A:

Q: Suppose T(x,y) = (2x, 2y) and U(x,y) = (x, -y). Is T∘U=U∘T?  Justify your answer.

A:

Q: If u = 2-x, J x/2-xdx%3D

A: Given: Let I=∫13 x2-x dx To Find: To evaluate the given integral by taking u=2-x.

Q: If u= 2i +3k and v = j– k, then

A: We will use formula for cross product of two vectors

Q: Question dz If z(x, y) = x²y, x = ", and y = u'v², find

A:

Q: Let ř =xi+y+ zk, and let u= ||F|I. 2-2u = 3ue. Show thet Dflu)= 6- 6u)e" r.

A: Given, fu=3u2e-2u. We have to show that ∇fu=6-6ue-2ur→ where r→=xi^+yj^+zj^.

Q: If f(x, y, z) = In(2 + x² – 2y² – 3z), 7 =, then Duf(2, –1, 1) = - A) * V3 B) 11 C) V3 D) E)

A: The given function is:    f(x,y,z)=ln2+x2-2y2-3z

Q: If u = -2i - 2j and v = 6i + 7j, find u - v.

A: We can solve this as follows: