Given f(x, y, z) = 4x2 + 2y? + 6z?, find %3D fa(x, y, z) = fy(x, y, z) = f:(x, y, z) =

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

Q: (2y – 3x)dx +xdy = 0 %3D

A: Find your answer below

Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

Q: Find the antiderivative F(x) that satisfies the given condition. dF dx = 4e* + 4x²; F(0) = -5

A: Given query is to solve the differential equation.

Q: Evaluate 3xz dV where E = {(x, y, z) | 1 < æ < 3, x < y < 2æ, 0 < z < x + 3y}

A: ∬∫Ef(x,y,z) dV = ∫x=ex=f∫y=cy=d∫z=az=b f(x,y,z)dzdydx                                where , E…

Q: Integrate f(x, y) = 4c®* - 0.5y using h = 0.5 with y(0) = 2 from x =0 to 0.5.

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Q: Use the linear approximation to f(x,y) = x+6 at (4, 3) to estimate 10.1 y+2 4.9 10.1 V 4.9 help…

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Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: fm üli f (x,y,z)=x'+x*y *z ' + yz ?

A:

Q: What is the integrating factor of 2y (y - r) dy = dr? %3D O y? 2y

A: Topic = Differential equation

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: Calculate fls f(æ, y, z) dS For 2² + y² = 16, 0 < z S ls f(x, y, z) dS =

A: Introduction: The surface integral is used in mathematics to add a collection of values associated…

Q: The output at a certain factory is Q(x, y) = 6x² + 3e36. ỹ+ 3y. %3D where x and y denote,…

A: The function is Qx, y=6x2+3ex36y+3y2. The marginal rate of substitution is given by dydx=-QxQy…

Q: Solve for the antiderivative of the function f(x) = C. *++3x + C A. ++9x+C B. 즉++9x +C D. 2x ++3x +…

A:

Q: Integrate f(x, y)

A: The region is defined as, Consider the conversion formulae from cartesian to polar coordinates,…

Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

A:

Q: Find the total differential. w = (3x + 4y)/(y + 3z)

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Q: the constant 'c' such tha 5y)âz + (y – 3x)ây z)âz

A:

Q: (* +y – 4z) dV where E = {(x, y, z) | 0 < y < 2, 0 < * < y, 0 < z < a +y?} Evaluate

A: ∫y=00∫x=0y∫z=0x+y2x+y-4z dz dx dy Now, ∫z=0x+y2x+y-4z dz =x+yz-2z2z=0x+y2 =x+yx+y2-2x+y22…

Q: A cylinder of radius r and height h has volume V = nr 2h.(a) Use the Linear Approximation to show…

A: Given: A cylinder of radius r and height h has volume V=πr2h a)  show:  ΔVV≈2Δrr+Δhhb)  Percentage…

Q: 4. 2a y' = y (y² + 3x?)

A: For the solution follow the next steps.

Q: Maximize the function f(x, y, z) = x² – y², given that x² + 2y² + 3z² = 1. %3D

A: Here, we can use Lagrange multiplier to maximize f(x,y,z)=x2-y2 with constraint x2+2y2+3z2=1. Let…

Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

Q: Compute fe F d where F (x, y) = x² + y). (2xy + x, Hint: Is F conservative?

A:

Q: Evaluate 3xz dV where E {(x, y, z) | 2 < x < 5, x < y < 2æ, 0 < z < x + 2y}

A: Given,

Q: Find the local linear approximation to f(x, y) = 4x² + y² at P(2,3)

A: We have to find the linear approximation of above function at (2,3) please see the explanation…

Q: Find relative extrema for f(x,y)=x^3 - 6xy + 8y^(3) - 2.

A: Question- Find relative extrema for  f(x,y)=x^3 - 6xy + 8y^(3) - 2.

Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

A:

Q: The fuel-cost functions for the three thermal plants is $/h are given by C, = 400 + 5. 5P, + 0.006P…

A: The given constraint: 50≤P1≤15050≤P2≤20050≤P3≤300 Where P1, P2, P3 are the loads of the generator…

Q: for w = x°y°z. dy Calculate

A: We have to find the partial derivative of the given function with respect to y.

Q: switch the order of integration, f(x, y) dy dæ

A: ConsiderI=∫-12∫0e-xfx,ydydx

Q: . Use the method of Lagrange multipliers to show that for x, y > 0, we have a" +y" > (팔1)" 2

A: We will first try to minimise (xn + yn)/2 using Lagrange multipliers then show that its minimum…

Q: Find the total differential. 2x + y W = 5z - 4y

A: For a function of two or more independent variables, the total differential of the function is the…

Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

A:

Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: Find fy and fy: f(x,y) = - 3 e 4x-5y f,(x,y) = D

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Q: F(x) = F' (2) , where (t4 - 3t2 )dt %3D d. Vt dt x2 dx

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Q: dy + ydx %3D = 3x²y?dx,

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Q: 16. If x x y and y x z, then how is x proportionally related to z?

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Q: Find the total differential. 5x + y w = 2z - 6y dw =

A: Consider the given equation. w=5x+y2z-6y The objective of the problem is to find the total…

Q: Given f(x, y) = - (4x°y + xy® ). Compute: dy?

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Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: Assuming that f(x) dx = 3, f(x) dx = 4, and f(x) dx = 8, calculate Fx) dx. %3D %3D Jo f(x) dx =

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Q: – 4z) dV where E {(x, y, z) | 0 < y < 1,0 < x < y, 0 < z < x + y²} Evaluate + Y E

A: We just need to put the limits and then integrate as following

Q: Find all values of x and y such that fx = 0 and fy = 0 simultaneously. 13. f(x,y) = e*»+y?

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Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A:

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

A: