Find values of x and y such that  fx(x, y) = 0 and fy(x, y) = 0  simultaneously. f(x, y) = 7x3 − 6xy + y3 smaller x-value     (x, y)  =                larger x-value     (x, y)

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: b) Find and classify all the critical points of f(x, y) = 3x²y + y3 – 3x2 - 3y2 +5. %3D

A: The solution is given as

Q: (x²y+2xy² x2+y2 (x, y) + (0,0) f(x, y) = %3D (x, y) = (0,0)

A: If the function is to be continuous at (0,0), then its limit should be equal to f(0,0) irrespective…

Q: 4 + 8z is The antiderivative of the function f(x) -4 4.0z +c 4. + 4.0z2 + c 4 | 4.0z? + c 8 + 2.0r2…

A: Using anti derivatives means integration.

Q: f(x, y) = 2x -y-e-* = 0 g(x, y) = -x +2y-e-y = 0 a) For X₁ = 1 and fx(x₁, y₁) = fy(x₁, y₁) = 9x(x₁,…

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Q: (2xy+ 3x2)e, +(x² – 2yz + 2y)e,- (e2 + y?)e, olan f(x, y, z)

A: Given that the function is

Q: pIV) – 9y "= 9 O 2y C + C2x + Cze 3x + C4e - x 3x O 2y C1 + C,x + Cze + Cịe" + x 3r 3x O y = Cj +…

A:

Q: 1 + (»*/x*)\ x² ) x + y 2.xy %3D (x + y) (x²+y²) + y(2y) y² - x %3D дудх (x² + y*) dz 1 %3D ду 1 +…

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Q: Solve for (x+y)*y’-y = 0 a. -2xy + y^2 = x^2 * ln(x^-2) + Cx^2 b. ye^(-x/y) = Cx^2 c. ye^(x/y) =…

A:

Q: Your major online bookstore is in direct competition with Amazon.com, BN.com, and BooksAMillion.com.…

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Q: (b) Use Gaussian elimination to find the values of x, y and z: x+2y+3z=10 -x+y+z=0 y=z=1

A:

Q: Find X Y Z for these equations 3/2 X + 2v3 Y – 32 Z = 15 - X +3 Y + 2 Z = e^0.5 V3 X + v2 Y – Z =…

A: For the system of equations AX=B, if inverse of A exist then X= (A-¹)B

Q: (1) E(x, -x)² =Ex} – nx² | (ii) E(x, –x)(y; -y)=Lx,y, – nxy (üi) E(x, – x)(y, – F) =Ex,(v, - )

A:

Q: (3x € X: (Vy € Y : E(x, y))) = \x € X : (³y €Y : ¬E(x, y)) ¬(Vx € X : (³ € Y : E(x, y))) = (3x € X :…

A:

Q: x = 2 - t, y = 1 + t, z = 3t; x - y + 2z = (x, y, z) =

A:

Q: 4) f(x, y,z) = /1– x² – y² – z²

A: Domain is the subset of R3 where the function is defined

Q: (2xy + 3x²)e, + (x² – 2yz + 2y)e,- (e2 +y²)e, olan f(x,y,z)

A:

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

A: It is partial derivative

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

A:

Q: f(z) = 3z + 5z -2 g(z) = 5z – 4z²+4. 5z - 4x2 +4 %3D Find (f + g)(z) O A. (f + g)(x) = 5x³ – 2² + 5x…

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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: (2r - y) dr- (r+ 4y) dy = 0 O 2y + xy-x = c O 2- 2ry - y = c %3D O - xy + 2r = c" O -x+ 2y +y = c

A:

Q: %3D iv) if zy = (x)-1 then z, + Zy = b.x+y c.-z (x+ y) d.z² (x- y) a.x-y

A:

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: 1- z Res z(z + 1). Iz=00 a) 0 b) 1 c) -1 d) 2 ||

A: Res( f, ∞) = - Res 1z2f1z, 0

Q: W = {(x, y, z), x² +y² + z² < 1}

A: W is not a subspace

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: 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: Find X Y Z for these equations 3V2 X + 2v3 Y – 32 Z = 15 - X +3 Y + 2 Z = e^0.5 %3D V3 x + v2 Y – Z…

A: We need to solve the given system of equations to find the value of x,y and z

Q: 2x + y + z = 1 X- y+4z = In1 x + 2y - 2z = 3

A: We will solve this equation with the substitution method. So first of all we will find anyone…

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

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Q: :Max z=6x + 8y subject to x +y 0, y=0.

A:

Q: (3) Let f(x, y) = 2xy? – x²y - 3.xy. Find the critical points. There are four critical points.

A: We have to find the critical points of the function of two variablef(x,y)=2xy2-x2y-3xy

Q: {(x,y): y=e}; {(x,y):y2e²}; (x,y): xy ≥ 1, x>0, y > 0.

A: This is a question from a real-valued function.

Q: Мaximize p = 10x + 10y + 15z subject to + z s 12 X y - 2x 2y + z 2 14 -y + z 2 4 x 2 0, y 2 0, z 2…

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Q: Differential Eqautions  a) y'''+2y''-5y'-6y=4e^x

A:

Q: Use the fact that the critical points of f(x,y) are found when Vf(x, y) = 0 to show that (-3,-2) is…

A:

Q: (2xy + 3x²)e +(x² – 2yz + 2y)e,y- (e² + y²)e, olan f(x, y,z)

A: Given

Q: 3. v+ 4)(v² + 8y)}v\y² + 8y – 1 dy y²+ 8y- 1 dy

A:

Q: find the first and second derivativ of y with respect to x y=x^3-9x^2+15x-5

A: Given:       y=x3-9x2+15x-5 First derivative:     differentiating with respect to x.…

Q: Let y=v,(x) y,+ v,(x)y be the solution of y"+p(x) y+q(x)y3D In(x), which obtained by the variation…

A:

Q: The number of defects on the front side (X) of a wooden panel and the number of defectsa on the rear…

A: Solution: From the given information, the probability mass function of X and Y is

Q: Find all the local maxima, local minima, and saddle points of the functions in Exercises 11-20.

A: (10)Consider the provided function, fx,y=x2+2xy Find all the local maxima, local minima, and saddle…

Q: Minimize c = 2x + 4y subject to 0.7x + 0.7y ≥ 7 2x + 4y ≥ 28 x ≥ 0, y ≥ 0.   min value c= occurs…

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Q: x=k y=1. kER 2=k x=1+k y=k ,kER z=1+k x=1 kFR

A: we have to find the parametric equation of the line that passes through origin and A(1,0,1).

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

A:

Q: Your major online bookstore is in direct competition with Amazon.com, BN.com, and BooksAMillion.com.…

A:

Q: arctan 2x 41. Differentiate y = x2{2x-(1+4x²) arctan 2x] (1+4x²) а. _x²[2x-(1+4x²) arctan 2x]…

A: We have to solve

Q: (b) f(z)= (4 – 5e*)³ x² + 1 (c) f(r)= ez %3D (d) f(z) = e=²–5z+4 ez-5x+4 (e) f(x)=xe² – e² = re² –…

A: We can solve this as follows: