a2u a2u 2y дхду a²u )Find du where ax - - axây' ay? u = x3 - 2x2 + 2y3 – 6xy + y ax2

Q: find ---y (a) u•v, (b) u•u, (c) ||v ||2, (d) (u• v)v, and (e) u • (3v).

A: Disclaimer: Since you have asked a question with multiple sub-parts, we will solve the first three…

Q: ▪1 2 6t5 dt du %3D 1 + t6 u | 2 %3D 1 II

A:

Q: Use Cramer’s Rule to solve…

A: The solution is given as

Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

Q: az az and at the point (-1, -3, -2). Suppose ry z - 94 = 4xy – z. Compute ду dz |(-1,–3,–2) az…

A: An important result from advanced calculus, called the Implicit Function Theorem,states the…

Q: Use Cramer's rule to solve for y without solving for x, z, and w. y + 5x + 3y 5х + z + w = -7 z + =…

A: Given:

Q: Solve Utt (1,4) Ux (o,t) =o UCX, 0) = 0 KUXX (xst) 0Lxo %3D Ux (1,t) = 0 Ut (x,0)= 2 %3D -1 %3D…

A: The given problem is to find the solution for the given wave equation partial differential equation…

Q: S = In sec 3x| + C 13. z sec² 3x dz %3D 3 - tag 3z,- å

A:

Q: f(x,y) = 3x-x- 2y ty faa(ay)= -6x fyy (3,9)= 123°-4 D(x.y) = faafyy-[tay]²- - 72ny² +24% ニ 12ay2+ こ…

A:

Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

A:

Q: dw Let w = cos(6x – 6y), where × = r* and y = 3. Find A o dw = 18sin(6r* – 18)r³ dt O dy =…

A: Answer is Option b is correct Explanationo the solution is given below...

Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

A:

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

A:

Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

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

A:

Q: 2x+ 3y-z =1 4x + y-3z = 11 3x-2y +5z = 21 | %3D

A: Solution:

Q: for w = ze(zy²+2:). Do not include =" in your answer.

A:

Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

A:

Q: Solve min udr, subject to u(0) = 0, u(1) = 1, ur'dr = c %3D =C.

A:

Q: Let f(z) = 5z2 + 3z.  Find u(x,y) if z = 8.2 + 5.9i

A:

Q: 9x + 2y + 4z = 20, x + 10y + 4z 6, 2x-4y + 10z =-15 54x +y+z = 110, 2x + 15y + 6z = 72, -x + 6y +…

A:

Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: Let X and Y be iid N(1,3). Let U = 4X + Y and V V_dependent or independent? Justify your answer. 2X…

A: Given X  and Y be iid with N(1,3). Mean, μ=1 Standard deviation, σ=3  U = 4X + Y and V = 2X — 3Y

Q: Compute Jx²z ds where C is the line segment from (0,6,–1) to (4,1,5).

A: The objective is to compute ∫Cx2zds where C is line segment from  0,6,-1 to 4,1,5

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y + z + = 7 5x + 3y z + 8 W…

A: Let's find.

Q: 2x+ 3y-z =1 4x + y-3z = 11 3x- 2y +5z =21

A:

Q: 6) MLATU = 45°, mZSTU = 120x – 1, and mZSTA = 73x + 1. Find x. %3D %3D T. U A

A:

Q: Compute ƒxz and ƒzz for ƒ(x, y, z) = xyz - x2 z + yz2.

A: Given that f(x,y,z)=xyz-x2z+yz2. We need to find : i)fxz. ii)fzz.

Q: If x + y + z = 12 & x² + y² + z² = 96 & !.!,!= 36 then value -+-+ -%3D X y of x³ + y3 + z³ is

A:

Q: Use Cramer's Rule to solve x + 2y + 3z 3r + 2y +z 17 11 I- 5y +2-

A: Given: The given equations are, x+2y+3z=173x+2y+z=11x-5y+z=-5 The objective is to solve the value of…

Q: Find Duf at P. 1 2. f (x, y, z) = 6x³y°z°; P(2, – 2, 2); u %3D - -

A:

Q: 7) If A = xz³i – 2x²yzj + 2yz*k, find VxA at the point (1,-1,1).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Express In x V in terms of in x, In y, and In z. 2mx-글 my-글 nz 2 Inx + 글 Iny-글 mz znx+my+nz In y 2nx…

A:

Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: Compute 1. % 1+ vår + g2 dr, lal 2 1+ " 2. 1+ V2r-

A:

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

A:

Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

A:

Q: 3. If V = (3r'y-1,x2'+y',-2r:"). Find grad divl at the points (2,-1,0).

A: We have to find grad(divV ) at (2,-1,0) where  V = (3x2y-z,xz3+y4,-2x3z2)

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…

A:

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

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

A:

Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

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

A:

Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

A:

Q: Uyy=4Uxx , U(0,y)=U(5,y)=U(x,0)=0 Uy(x,0)=3sin(2pi x)x)-2sin(5pi x), y>0

A:

Q: me succe LO SUIVE uie folnoWing 2 и (х)— | (x -t )u (t )dt 2 --

A:

Q: Q)is a) x^2=y^3 reflexive antisymmetric Transitive  Explain it correctly,solve only when know…

A: We have to find the correct option