8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2и + 3v (b) |u| (c) u-v (e) |v X w| (d) u X v (f) u (v x w) (g) The angle between u and v (rounded to the nearest degree)

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Q: z = x2 + xy4, x = uv? + w°, y = u + ve" dz when u = 3, v = – 2, w = 0 dv then find:

A: Solve by partial differentiation

Q: 6. Given that z = u' + 2v – x + 3y; u = r´ - s', v = r´ + s´, x = 2rs, y = 4. Find 2 =r dz(r, s, h,…

A: Given, z=u2+2v2-x2+3y2u=r2-s2 v=r2+s2x=2rsy=2rsTo find: dz(r,s,h,k)

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Q: 5. Suppose z = f (x, y), where x= g(s,t)and y= h(s,t). Show that ôz d²x ¸ ôz ô²y %3D ô°z ôx ôy ôz(…

A: Chain rule of partial derivatives: Let us consider a two variable function  z=f(x,y)  where ,…

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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.

Q: 14. Find the distance between the two skew lines. x = 2+t x = 4+s y = 3-t y=1+s z = 4t z = 2- 2s

A: Given query is to find the the distance between two skew lines.

Q: The equations re + uz – cos(v) - 2 = 0 and u cos(y) + 10x2v – 10yz2 – 1 = 0 can be solved for (u,v)…

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Q: Ut + 4tuz – 2u e', x E R, t > 0 u(x, 0) xe- , x E R. Find u(x, 1).

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Q: 4. Evaluate fo (3x + y)dx + (2y – x)dy along the straight line joining (0, 1) to (2, 5).

A: We need to find the line integral ∫(0,1)(2,5)3x+ydx+2y-xdy .  We first parametrize the line segment…

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Q: 8. The distance between the planes 2r-y-2z 5 and 2r – y - 2z = 7 is A C 2 9 dn 24

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Q: 5 Jlgu ntinuity equation satisfied by u= 3x^2-2y^2, v=-6xy IO 4xy+y?, v= 6xy+ 3y .II O U = u=x-4y,…

A: We have to solve given problem:

Q: Solve the Neumann problem Ди — 0 Uz(0, y) = 0, Uz(7, y) = D, cos(ny) Uy(x, 0) = 0, u,(x, T) = 0 0 <…

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Q: ( Deterauine fiie value of x So fhct e will be parallel to live m. CRefer to Test#2 Problams #13 3/4…

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Q: 15. In AXYZ, XY YZ and m/XYZ = 46*. %3D 46

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Q: (1,1) = H dy =1(2y - y*)3 - y*| dy =, (8y* – 12y* + 6y5 - y6 – y")dy =(8y - 12y' +6y" – 2y) dy =(4y…

A: Ix and Iy denotes inertia about x-axis and y-axis  Ix=∫∫Ay2 δ(x,y)dA  and Iy=∫∫Ax2δ(x,y)dA And…

Q: If V = (3x + 2z²)i + j- (z – 7x)k then V. V at the point. (1, 1, 1) is ||

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Q: f(x, y, z) = sin(ry + z) foksiyonunun| P(1, 7/4, 7/2) noktasinda v = -2i + j+ 2k

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Q: 3. Find dz/Ou and dz/du. (a) z = 9x*y- r+ 5y; X = UV; Y =v – u (b) z = 2e*". 1 a= vuv: y=

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Q: 3. Eliminate the arbitrary constants c, and c, from y =c, +C,e* y" - y +x = 0 c. y" - 3y' = 0 a. b.…

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Q: 1. The lines 4: x=1-t, y=2+t, z=-2-t; 12:x=3+s, y=-1+s, z = 2s are skew.

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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: 2. W =I+xy- Z finds Wzz WZX NJ 3.

A: Given W = 1 + xy2 - z2

Q: 8. Calculate the given quantity if u = i+j- 2k v = 31 - 2j + k w = j- 5k (а) 2u + 3v (b) |u| (c) u-v…

A: Hello, thanks for the question. Since we only answer up to 3 sub-parts, we’ll answer the first 3.…

Q: 4) Solve via separation of variables: u(0, y) =0 ди -(2, y) = 3sin a'u a'u +5 sin =0 ; 6. S0<x<2…

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Q: In x - direction (+ -) - Fu + P,A,- P3A3 cos 40° m, V, cos 40° - m, V. F = P1A,- P3A, cos 40° + m,…

A: To identify for True or False.

Q: If f(x,y) = 3e2y cos (x-2), then the linear approximation at (2,0) is %3D (A) 3-3x (B) 3+ 6y (C)…

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Q: QI. Solve the following problem with insulated boundaries: U = Uxx Ju,(0, t) = 0 lu(1, t) = 0 u(x,…

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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: 3. (z, y)(1.5x, 1.5y) A' will be located at ( B' will be located at ( C' will be located at (

A: We have given the scalar factor i.e . (x,y)=(1.5x,1.5y)

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A: Given: x,yRz⇔z=xVz=yx,ySz⇔x-y22+z2-x22=0

Q: If f(x, y) = 3e-2x cos (y – 2), then the linear approximation at (0, 2) is (A) 3 – 3x (B) 3+ 6y (C)…

A: A function of 2 variables can be linearized using the partial derivatives. The formula for the…

Q: The solution of y" = 8(t – 1) – 6(t – 3), y(0) = y'(0) = 0 is y(t) = %3D (A) (t- 3)[u(t - 1) - u(t-…

A: Given y''=δt-1-δt-3, y0=y'0=0

Q: x+2 السؤال الثالث: جد ناتج التكامل (x - 4y + y* z)dydxdzباستخدام التحويل v =, u = 4y – x, W =

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Q: Find Duf at P f(x,y,z)=4x^3y^3z^3;  P(1,−2,1);  u=1/3i+2/3j−

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Q: The solution of y" = 8(t – 1) – 8(t – 3), y(0) = y'(0) = 0 is y(t) = (A) (t – 3) [u(t – 1) – u(t –…

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Q: 5z g(x) = J. u + 4 du 7z u? +1 = (x),6 HINT: 5z u + 4 du u + 4 u + 4 du -du + u? +1 /7z u² +1 u? +1…

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Q: The solution for the IVP: Uxi u(x, 0) =2 x u,(x, 0) -ex. ux, () - 2x + (*-0-(**) O b. u(x,…

A: Consider the given information. utt=uxx                 -∞&lt;x&lt;∞t&gt;0ux,0=2xutx,0=e-x D…

Q: If f (x, y) = V3 + y³ In (z +y°)e*in(zyty") +2² + 10y , then fz (1,0) = |3D %3D O 2 4. O 3

A: Given that fx,y=x3+y33lnx2+y2esinxy+y2+x2+10y3 First we have to find fxx,y where fx=∂f∂x

Q: 9(x, y, z) = xy + xz + yz; C: r(t) = (1, 21, 3t) , for 0<i54 %3D

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Q: س/ أختار قيمة R ,D المناسبة ل لداله الاتية f(x) = 2 + Vx? - 1 Df = {x:xeR:x 0} O الخيار رقم 1 D, =…

A: The given function is fx=2+x2-1. Calculate the domain and range. Range is defined the all possible…

Q: L'équation 5xyz = 2x2 + y² +2z² + 6 définit implicitement z comme fonction de x et de y au voisinage…

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Q: I ntegrate: Sv V v+2dv HIN T: If u =x+Q, then × = U-a

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Q: 12. Obtain the general solution of (D4 + 16D² + 63)y = 0 a. y = c,cos v7x + c2sin /7x + c3 cos 3x +…

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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: 16. f(x, y, 2) = y - Vr? + z?; P(-3, 1, 4); a 2i-2j-k

A: To find the directional derivative of f at P in teh direction of a So, given f(x,y,z)=y-√(x²+z²);…

Q: ='i+(2xz - y)j XZ and (2, 1, 3) is

A: