If 6(x, y, z) = x?yz3 and A = xzi -y²j+2x²yk, Determine : www a) V X 4 b) VX A c) V X (p.A) d) A x (V x A) at point (1,-1,1) e) V X (V x A) at point (0,1,2)

Q: (b) If z r+ry- y7, 1= u+ and y = 2uv, find: in terms of du %3D u and v.

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Q: Calculate ∬Sf(x,y,z)dS For x^2+y^2=9,0≤z≤3;f(x,y,z)=e^(−z) ∬Sf(x,y,z)dS= ?

A: Find the parametric equation for the given curves.

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

A: We wil find the second order partial derivative.

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A: To evaluate ∂w∂r

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Q: If (x, y, z) = x²yz³ and A = xzi -y²j + 2x²yk, Determine : ww a) Ax (Vx A) at point (1,-1,1) b) VX…

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Q: Find the line of intersection of the planes 2x – y+ 3z = 1 and -r + 3y + z = 4. Lütfen birini seçin:…

A: Given planes are 2x−y+3z=1 and −x+3y+z=4. We have to find the line of intersecting of the plane…

Q: If x,+iy,=x,+iy2 then x=y, %3D

A: TRUE for part (1) It is given that x1+iy1=x2+iy2. x1+iy1 and x2+iy2 are complex numbers Two complex…

Q: b) Show that the implicit Trapezoidal method h Wi+1 = Wi +5 f (ti+1, Wi+1) + f(ti, w;), is…

A: The solution is given below in the next step:

Q: Lous on C, then )dS =r P(h(y,z), y, 2) /h3(y, z) + h?(y, z)+1 d. P(h(y, z), Y, z) Vh3(y,2) + h? (y,…

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Q: Show that d(y,u)/dv = (1– v²/c)3? for y, = 1//1- v²/c?. %3D

A: Given: γv = 1/1 - v2/c2

Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: Prove or disprove: Vx € Q, Vy e Q, 3z E Q, (x < y) → (x < z< y).

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Q: f (x, y, z, u, v, w) 3æyzuvw + x²y²w? – 7cz° + 3yvw Calculate [af af af af af af + for a = y= z = u…

A: Solution

Q: 3. Bir f (1,y, 2) = ee cos 5z fonksiyonu veriliyor. a) grad f (r, y, z) =? bulumuz. b) Bu…

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Q: 4. Which would not be sufficient to prove AWXZ ~ AWYX? C ZWXZ = ZY WZ A WX XW %D YW XY WZ XZ WX Y WX…

A: In both the triangles angle W is common so for similarity using SAS property:  WZWX=WXWY OR…

Q: This question is from partial differential equation please sir g give me answer immediately

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Q: Given f(2, y, z) =v V-I - 2y + z, find f.(z, y, z) = f(z, y, z) = f(1, y, z) =

A: We will use definition of differentiation. First we will handle derivative of the root of the…

Q: The distance between the following two skew lines is Line#1: [x, y, z] = [1,1, 10] + t[5, –3,0]…

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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…

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Q: How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1…

A: Solution is given below:

Q: Calculate ∫c (2 + z) ds, where Basket given by r (t) = 4/3t3/2i+1/2t2j+tk, 0≤t≤1

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Q: 8. % = () Given that u = and w = calculate the values of x and y if 2u = v - w. %3D

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Q: If VW = -2z + 29, UX = z + 9, and ST = z + 13, what is UX? %3D V U UX w/ ト

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Q: O Civen w (2-31, XL-4,9),Y(S,y) and z(-1,1) find the Value so that ux LYZ

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Q: Differentiate the follo ear and non-linear. w +z =2 1. x +y- z= G X +v-

A: (i) First we differentiate the given equation with respect to x: xy+z=2⇒ddxxy+z=ddx2⇒y+xdydx+dzdx=0…

Q: Be z = (x-y)/(x+y), where x = (u/v), y = (v2/u), calculate ∂z/∂u and ∂z/∂v

A: The given equation is z=x-yx+y where, x=uv, y=v2u. Find the value of ∂z∂u and ∂z∂v. Here we use the…

Q: Show that if f(x, y) is homogeneous of degree n, then                                     xfx(x, y)…

A: It is given that fx,y is homogeneous of degree n,

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: af(x, y) If f(x, y, z) = , then is equal to dz (y – 2)² (y – 2)? O 1 2z – x – y (y – z)?

A: Given problem:-

Q: 5={cj+ kn, u +vn): nez T={(x,y)EZ:157 x +107 y =- 157 x +107y=1 choose j,K, u,v EZ, such that S=T"…

A: Linear Diophantine equation: A linear Diophantine equation in two variables takes the form of…

Q: Let z = 3x*y, find Vz.

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

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Q: If ø(x, y, z) = ry²z find grad ø at (2, – 1, 3).

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Q: Enclosed by the cylinders z= x2 y = x 2 and the planes  z =0 y =4

A: Given: The cylinders z= x2 y = x 2 and the planes  z =0 y =4 The solid enclosed by the surfaces,

Q: Show that there are point(s) (x, y, z) satisfying 2x − 3y + z − 5 = 0and lying on the line v = (5,…

A: The given equation of the line is

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

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

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

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

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Q: If y (x, y, z) = x² + y? + z² and A (x, y, zis perpendicular to Vy (x, y, zeverywhere, wh…

A: Perpendicular vector field

Q: az au əz əv əz ?w 11 11 || z = x² + xy³, əz əz du av az aw x = uv³ + w², y = u + vew when u = 1, V =…

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

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Q: If p is the distance between the skew lines 4,:x=1+t, y=1+6t, z=2t Lz.x =1+2f, y=5+15f, z=-2+6t,…

A: Shortest distance between two skew lines

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: