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

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: 7x – 4xy = C

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Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: Find the max and mins of the following function using Lagrange multipliers f(x, y) = x° + y° subject…

A: Given: fx,y=x3+y3gx,y=x2+2y2-36 Find partial derivative of f and g with respect to x and y, fx=3x2,…

Q: A large but sparsely populated county has two small hospitals, one at the south end of the county…

A: "Since you have posted a question with multiple subparts, we will solve first 3 sub-parts for you.…

Q: manufacturing company employs two devices to inspect output for quality control purposes. The first…

A:

Q: 4. Find the branch points of the following functions and indicate a suitable cutting. a. fi(z) =…

A: (a) Consider the given function as, f1z=2z2+1

Q: ) If ƒ(x,y) = 3x²y + cosy+ ysinx – e2x then verify fxy = fyx

A: fx and fy are the partial deferential of function w.r.t x and y respectively. Then fxy is the…

Q: Consider thế iñifial a. 2y"- 30y" + 150y' – 234y = 0, b. y"+ 6ay' + (9a² + 1)y = 0, y(0) = -3, y(0)…

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Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

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Q: 1. Show (in terms of e – 6) that a function f : [2, 7] → R be defined by f(x) = Vx² + 1 is uniformly…

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Q: Find the adjoint of F:C3 tends to C3 defined by F(z1, z2, z3)=(2z1+(1-i)z2 , (3+2i)z1 -4iz3 ,…

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Q: 6.5.4 Find the PDF of W = X + Y when X and Y have the joint PDF fx,x(z,y) • otherwise.

A: Given: The joint probability density function of the random variables X and Y is provided as:…

Q: Find for following 1.y = (x + v3x)S

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: (8) Suppose f(x, y) = -x + y², x = s² +t°, y = 2s – 3t. Compute f, when s = 1 and t =-1. %3D

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Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

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Q: [2] Show that the functions f (x) = 4x" , and f,(x) = x*+* linearly independent (-00, 00). are on

A: To Show: Show that the functions f1x = 4xn, and f2x = xn+4 are linearly independent on -∞, ∞…

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

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Q: 2. Suppose the PDF of X is given by fx(x) = 5e-5x(o)(x). Find its CDF.

A: Solution

Q: The function y== In (3z - 2) satisfies the IVP: (3z – 2)°y" + 9 = 0, y(1) = 0, y'(1) = 8. Select one…

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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: Find the best rank 2 approximation to A from (1) with respect to ||:||F.

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Q: A function e : X → Y is an embedding if one ond for V

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Q: 8 Ay 10- Compute the following estimate of f(x) dx using 8- y = f(x) the graph in the figure. 6-…

A: Consider the graph of the function

Q: 2. Compute P, and Py as a function of x, y, P.

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Q: Let D, be the linear transformation from C'(a, b] into C[a, b]. Find the preimage of the function.…

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Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

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

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Q: 12. Show that F (x, y, z) = xy +xz + yz has the value 1 if and only if at least two of the variables…

A: This Question is From Boolean algebra where + sign denotes or Operation. So F(x,y,z)=xy + xz+yz if…

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: Let, T: R3 → R³;T(x, y, z) = (2x + y, y – z,2y + 4z) Find the rank and nullity of T.

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Q: The critical Points of f(x, y) - x' -3x +3y2-6y are: None of these O (1,1) and (-1,1). O (01) and…

A: We will find the first order partial derivatives of f and equate them to 0 to find the critical…

Q: 2. Use a linear approximation to estimate V1.03. 3 If f and a are the functions whose gronhs

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Q: Let RC [0, 1] ×x [0, 1] such that (x, y) E R (i.e., xRy) whenever 4x < 6y < 9x . Deter- mine if R is…

A: R is not a function, because there can be multiple ordered pairs with the same first coordinate,…

Q: 1 Let f (x,y)=In . Then f „(1, – 1) =...... 3x²+4y3 XX

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Q: 1. Find the optium path for f=xy³ from (2,1,2)

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Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

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: Lqsudnhlao203=9m] -03P99E90RO[9U3RM7210 Ud8y(,om 301 29u 3 ***#!12ngwe gggd 982eh c y The function…

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: Let f(x,y) = x - 5xy -y². Compute f(6,0), f(6, – 2), and f(b,c).

A: Solved below

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

A: Differentiate wrt y.

Q: 5) Let z = f(x2 - y²). Show that y = 0 ду %3D ax

A: Here, ∂ represents the partial derivative, which means when differentiating with respect to x,…

Q: 1. (12 points) Consider f(x, y) = xy2e". Compute the following: (a) af (b) af dy

A: To find the partial differentiate with respect to x, y remains constant and vice versa.

Q: let 2.+ (3(x-1+4y+!j". ニ ): find the Critical points f f.

A: In the question we have to find critical points.