If f = ux+v-y, g=u²+vy+ w and O(f.g,h) ô(11,v, w) h= zu -v+ vw compute

Q: If u=f(x2+2yz,y2+2zx).Prove that

A: Given: u=fx2+2yz, y2+2zx Let u=fv, w where v=x2+2yz and w= y2+2zx. Now prove…

Q: If f(z) = 10 V 824 - 2° + 5, find ƒ '(x). %3D O f (z) = 5 (8z“ – 2z° +5) *| O f (z) = 5 (32z° –…

A: The given function is fx=108x4-2x6+5. Differentiate the function with respect to x by the power rule…

Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

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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: 2z + 5z + 14 If U(z) = evaluate u %3D Uz and (z – 1)

A: Solution :

Q: Verify that det A = det B + det C, where Uj + vj U2 + v2 Uz + V3 A = A22 аз1 A32 --EE-E: A12 A22 V2…

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Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find the linear approximation to ƒ at P0(1, 2,…

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Q: Verify f U= n1 V = 234 43 snyz %3D +23- 422-24-42- dependend %3D fundlarelly are

A: We know the identity: x3+y3+z3-3xyz=(x+y+z)(x2+y2+z2-xy-yz-zx) --(1) We are…

Q: xy If z show that: x- y

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Q: Use chain rule to find az at (u, v) = (1, 1) if

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Q: Which elements are invertible in Z4[x,y]?

A: W need to find elements which are invertible inZ4x,y.

Q: Compute x 2z ds where C is the line segment C from (0,6,–1) to (4,1,5).

A: The given line segment from   to   can be represented parametrically as: , , and , for    Using the…

Q: Suppose that (Q x Q, +,.) is a ficld where (x, y) + (z,w) (x+z,y + w) and (x, y). (z, w) (xz +2yw,…

A: I have find identity of the field and then inverse

Q: Find the aven bounded by y=x and y =x+2

A: First draw the graph of the function and find the intersection point of the graph:

Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

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Q: 14 Verify the given linear approximation at a = 0. Then deter-

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Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

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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: 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: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: 1. For U, iid uniform on (-0,0) show that - min, {U,} is sufficient for e > 0.

A: # given ui follow  uniform distribution (-theta,0) then to show that -min(ui) be the sufficient…

Q: Let f(x, y, z) = x²y°z – xyz², and compute: (a)

A: In this question we will use basic of vector  calculus i.e gradient of any function and curl of…

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: The function f (x, y, z) (3, 0, 0), (0, 2,0), (0,0, 6) and (1, , 2) What is the value of a? = xyz…

A: To find the critical points of the function f(x,y,z), subject to the the constraint g(x,y,z), apply…

Q: Suppose that U(x; y) = xe' + ysin z, and that x, y and z can be measured with maximum possible…

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Q: Let f be q functiom that admits contırous second partial denvatives Df (X.Y)=(4x²- 2q²x+ 2q°y ,4y³ +…

A: Given, the second partial derivatives              ∇f(x, y)=4x3-2a2x+2a2y,  4y3+2a2x-2a2ywith a>0

Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: Minimize c = s + t + u subject to 3s + 2t + u ≥ 48 2s + t + 3u ≥ 48 s + 3t + 2u ≥ 48 s ≥ 0, t ≥ 0, u…

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Q: 3. Compute fc F · dr where F(x, y, z) = (x+ yz, 2x, xyz) where C consists of the segments from (1,0,…

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Q: Suppose that the share of total production consumed by player i is x / x+(n1)y, where is player i's…

A: The utility to player 1 is given as: u=xx+n1yAnw-x-n-1y;w>0,A>1 Also, Ak=Aw-x*

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

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: Let f(r, y) = 5x-+ 2y + 4y- 8ay List the critical point:

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Q: In Exercises 47-50, verify that wy Wyx- 48. w e+ x In y + y Inx

A: To find the second partial derivative of any function z i.e., zxy first differentiate z partially…

Q: 10. Show that 1/x, x are linearly independent on (0, 0).

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Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y…

A: We have find the jacobian

Q: Question #30

A: Note: Some of the basic calculations are directly written due to the question being very lengthy. We…

Q: Minimize c = s + t + 2u subject to s + 4t + 2u ≥ 95 4s + t + 3u ≥ 95 s ≥ 0, t ≥ 0, u ≥ 0. c= (s, t,…

A: the given simplex problem is as follows  Minimize c=s+t+2u subject to…

Q: Compute I ds over the path C : F(t) = (t, 2t,ť²) from (0,0,0) to (4, 4, 4).

A: The answer is given below:

Q: You invest to maximize utility: U = a, -À

A: Given information: The information ratio is 0.5. The risk aversion parameter is λ = 12. The utility…

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

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Q: 1 If f(x, y,z)= of then x- y- 3z ду

A: Differentiate wrt y.

Q: Suppose z = f(x,y) where x = Puv and y=u+tv². Given that z,(4,3) = 4 and z,(4,3) = – 1. Compute z,…

A: Explanation of the answer is as follows

Q: 6. Compute fxyx (1, –3) and fyxy (1,–3) for f(x, y) = (x + y)*.

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Q: Suppose that w = f(x,y), x(s, t) = . = y(s, t) = And that fx(1,1) = 3, fy(1,1) = 4, fx(2,2) = 5,…

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