If ƒ(2)=z²+1 then u(x,y) = 3+y² 3- y² + 1 83+y²-1 3- y²

Q: Find fx, fy, Tz (3x2 + y2 + 2z²) f(x,y,z) = e - fx=

A: f =e-3x2-y2-2z2  For fx ,we take y and z as constant and x as variable.  fx=∂f∂x For fy , we take x…

Q: f(x, y, z) = 3x - 2y + z- 12 = 0 g(x, y,z) = 4x + 2y - 25 = 0 h(x,y, z) = x- y²z-7= 0

A: Use the following formulae, to find the approximate solution of the non-linear system by the Newton…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = 1 + xy2 - 2z2

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Q: If f(x,y,z)=x²y³-y²z³ Then f;= -3y²z2 Jlgn

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Q: 1 max z = 2x, + x2 - x1 + x2 s 1 Xị + x2 s 3 s.t. 2x2 < 4 X1, X2 2 0

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Q: if z=x+iy then zz= 3- y² +1 3- y² – 1 G- ² |

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Q: If f(x, y) 2x+6 %3D of then is given by: (2x-6y) 24 (2x-6y)2 24 (2x-6y)2 12 (2z-6y)2 12 (2x-6y)2

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Q: y′′ + 2y′ − 8y = 2e-2x − e−x , y(0) = 1, y′ (0) = 0.

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Q: 1. X 8-2y (T, S) 2x+3y = 13 2. 5x-2y =-7 (C, A) X = -2y +1 3. X=-2y-2 (N, K) 2x +5y = -7 4. Y=-19-3x…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: What is the particular solution for y′=−2e^x−3x^2+x−4 such that y(0)=1?

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: Max z = x1 + x2 s.t. 2x1 + x2 ≤ 20 x1 +3x2 ≤ 15 x2 ≤ 4 x1, x2 ≥ 0

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Q: Obtain general solution of y' = y + y^3.

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Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

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Q: If y is a solution of y"+xy'+3y =0 then find the

A: Find y' and y'' from the equation y=∑m=0∞ amxm .                                       y'=∑m=0∞…

Q: Compute (T2 T)(x, y). T(x, y) (3x, 7y), T2(x, y) = (x-y, x + y)

A: We have to find T2 composition T1 .

Q: [x² - y² If f(x,y)=2x-2y m if y = x if y=x then:

A: Given the function,   fx,y=x4-y42x-2yif y≠xmif y=x

Q: y + z = 6, x + 2y +3 nsistent, if λ is

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Q: z² - xy = 2 at the point (2, 1)= %3D

A: We have to find the slope of the line tangent  to the given curve.

Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: 2. T1: R2 - R2, T1(x, y) = (x – 2y, 5x + 2y) T2: R2 - R2, T2(x, y) = (0, x)

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Q: Зх — 4у + 23 (a) f(x, y, z) = '9 – x² – y² –. - V2t – 4 x² – y? - (b) g(x, y, t) : -

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Q: S (x,y.:)= 4x°y° -e°y* ++4y-x" +4y–x'6

A: It is partial derivative

Q: Find fxy(x,y) if f(x,y) = (x² + y²)6.

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Q: f (x, y, z) ) = x² + y² + z²; x* + y* + z* = 1 2. 4 || ||

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Q: Find the general solution to(D5 - 2D³ – 2D2 – 3D - 2)y=0 O y= e-X(C1 + C2x)+ C3e2× + C4cosx+ C5sinx…

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Q: Find y' for x^4y^3−3x+2y=24 at the point (−2,1).

A: We have, x4y3−3x+2y=24 Using the chain rule of differentiation,…

Q: z = xy³ – a²y, x = t² + 1, y = t2 – 1

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Q: .2 f(x, y, z) = 4xy – 8xyz + 7yz² f,(x. y, z) = &xy– 8yz fy(x, y, z) = | 4x- - 8x2 f.(x, y, z) =…

A: To find the first partial derivatives of: f(x,y,z)=4x2y-8xyz+7yz2

Q: 2x +y-z=3 x- y+z=0 y+2z =1. Then x=

A: Given system of linear equations; 2x+y-z= 3 x-y+z = 0    y+2z=1 We can use Cramer's rule to solve…

Q: How would you interpret the coefficient of β2 in each model? Ln(Y) = β0 + β1 Ln(X1) + β2 Ln(X2) +…

A: Note : Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Given: xIn y + y²z + z² = 8 Find: дх дz -(x + 2y² z) y(y² + 2z) -y ln y x + 2y² z - In y у2 + 2z -у²…

A: Let's find derivative of given function.

Q: fx (x, y)=-2xety-x²-y- fxx (x, y)=-2e4y¬x²-y² + 4x²e4y¬x²¬y? fy (x, y)=(4 – 2y)e+y¬x²-y² fyy (x,…

A: Here we have to determine that how did he get derivative. We have,…

Q: 3x + 11y af If f(x, y) = then is : 3x – 11y dy - 66x (3x + 11y)² 66x (3x – 11y)² 66x (3x + 11y)2 66x…

A: Partial derivative

Q: V1-x2 3. Evaluate S S /1-x²-y² dxdydz V1-x2-y2-z2

A: We will solve the following.

Q: 3x3+y² x²+y² .2 (x, y) ± (0; 0), ,2 ) f (x, y) = 1, (x, y) = (0; 0).

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Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

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Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

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Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 1–10.

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Q: b) Give a particular solution for y" – 2y' + y = et - 1+x2

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Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

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Q: max x+ y2 + z² subject to x2 + y² + 4z² == 1 and x+3y + 2z = 0

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Q: Find y' for x^2y^4−3x−3y=13 at the point (−1,2)

A: Given Data: Equation: x2y4-3x-3y=13 Point: x, y=-1, 2   Differentiate the above equation with…

Q: Find the general solution to(D5 - 2D3 -2D² – 3D – 2)y=0 O y= e-X(C1 + C2x) + C3e2X + C4cosx + C5sinx…

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Q: 3 18. z= 19. y= Vx(x-1) 3x-1 20. y= 2x+1

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Q: x²y-y -y': у+1 ; у(3) - -1 %3D а. х3— х — Зу- Iny3 - 21 %3D с. х3 — Зх - Зу- Iny3- k d. x3 - 3x -…

A: Given that : y' = (x2y - y) /(y+1).and y(3) = -1. We solve this differential equations by using…

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

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Q: 4) Determinė the equation of the tangent to f(x) = -x² + 3x+1 that is perpendicular to the line x+2.…

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Q: x - 1 = λχ y = 2 = λy z = -λz (x² + y² = z² = 0,

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Q: Evaluate B: А: Vye-y° dy 3e-4z2 dz 0, 0,

A: There is a general integral that gets calculated with the help of β function. The integral is…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.