Find of, of and az дх ду HINT [See Example 3.] 24 f(x, у, 2) x2 + y2 + z2 af ax af %3D ду af Find their values at (0, -1, 1) if possible. (If an answer is undefined, enter UNDEFINED.) Of (0, -1, 1) = ax Of (0, -1, 1) = ду af Но, -1, 1) %3 az

Q: Suppose that f.(4, 5) = fy(4, 5) = 0 and frr(4, 5) fyy(4, 5) = [fry (4, 5)]². Then the second…

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Q: z = f(st - 3, s2 +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9) =…

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

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Q: If Z(x1(n))=X1(z) and Z(x2(n))=X2(z) then what is the z-transform of correlation ?between the two…

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Q: 4メーY - 3z = -8 -x+3y - 2z =5 2x + 2y -5z =7 ニ

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Q: Find the linearization of ƒ(x) = 2/(1 - x) + √(1 + x) - 3.1 at x = 0.

A: Here The formula for the linearization is Here a = 0 Therefore,

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Q: 1) A (2, 5) and B (4, 3) V (x2 – x1) ^2 + (y2 – 1) ^2 V 2) F (1, 7) and G (6, 0) V (x2 – x1) ^2 +…

A: If we have given the coordinates of two points then we can easily find the distance between them…

Q: 5)Let w-f(u, v), where u = X -y andv = a) Using the chain rule, express x-y in terms of x, y, of and…

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Q: Use the Wronskian and any needed theorems to show that f1 = sin x + 2x2 and f2 = e3x are linearly…

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Q: The Wronskian 1. Show that the functions ex, cos x and sin x are linearly independent.

A: As per guidelines, We’ll answer the first question since the exact one wasn’t specified. Please…

Q: For x = 1, 2, 3 and y = 1, 2, let the joint pmf of X and Y be defined by f X,Y (x, y) = (x+y)/21…

A: The joint probability mass function of X and Y is  f(x,y)=(x+y)/21   , x=1,2,3 and y=1,2

Q: Let X₁, X₂,..., X be a r.s. from N(,0) and Y₁, Y₂...., be another independent r.s. from m…

A: Solution

Q: Let f(x) = 3x² and. P = {–2, –1, 0, 1, 2, 3}. Compute Lf(P) and U,(P). %3D %3D

A: Consider: fx=3x2 and P=-2,-1,0,1,2,3. Compute LfP and UfP.   If P is a partition such that…

Q: Use Theorem 2.4.1 to prove that f(x,y) = 1 - x^2 - y^2 defined in R^2 is concave.

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Q: Sve SVé -3 dt u = Ve' – 3

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Q: 4-Find the coordinates the front trace F for line AB, if A(2, 1, -2) and B(3, 3, -5). * O (1,-1) O…

A: A=(2,1,-2) B=(3,3,-5)

Q: Find the values of a, b and c that make F=-5y°z7 (ax + bx6ji - 45,8,7(4x10, 107j+ cy°z64x10, 10x7jk…

A: Given that                          F=-5y9z7ax9+bx6i-45y8z74x10+10x7j+cy9z64x10+10x7k we know that…

Q: If var(X) = 2, var(Y) = 5, var(Z) = 1, cov(X,Y) = 2, cov(Y,Z) = -1, and Xand Z are independent, find…

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Q: Vr+2+Vx-2 If a = prove that a -ax +1=0 Vx+2-Vx-2

A: To prove , we need to simplify the left hand side of the equation till it becomes 0. To do this…

Q: 2x+ 3y-z =1 4x + y-3z = 11 3x- 2y +5z =21

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Q: f" > 0 on (-∞, -1) U (-1,0).

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Q: Suppose X1, X2, and X3 are independent and N(0.1)-distributed. Com- pute the moment generating…

A: Given function Y= X1X2+X1X3+X2X3 We have to calculate moment generating function

Q: X, + x, +x3 - 2x, = 2 2x, — 3х, + х, — 4х, 3 6 x, + 2x, – 3x, + 4x, = -5 denklem sistemini Cramer…

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Q: Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

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Q: Let f(x, y, z) = yexyz², then fxz is: Select one: O (4xyz + 2x²y³z²)exyz² O None of these O (2xy² +…

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Q: Find (T3 • T, o T1)-1 if Ti 1(х, у, 2) %3D (х - у, — у, х+2) T."(х, у, 2) %3D (х -у+z, 0, 3x) T(х,…

A: This question is related to linear transformation . See 2nd step.

Q: 1- -Н(y)-Н(yх) Prove that 2- H(x,y) = H(y) + H(x\y) 3- H(x,y) = H(x) + H(y}x) 4- Н(х., у) %3DН(х) +…

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Q: Let v1 = (1,1,2) v2= (-1, 2, -2) v3= (-2,-1,1). Write u = (6,7,2) as a linear combination of v1 v2…

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Q: Let u and v be defined implicitly as functions of x and y by the equations xv + yu 5 x² – y3 + uv² =…

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Q: find absolute max and min of x^3-3xy+(y^2/2) in region (0,0) (4,0) (0,5)

A: We have to find absolute max and min of x3-3xy+y22 in the region (0,0) (4,0) (0,5)

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: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: 5. Compute the solution to the original system of equations by transforming y into x, i.e., compute…

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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: You are given 6 data points (xi; yi) below, where i = 1,..., 6 that are observed from a model: y =…

A: Given information: Given data represents the values of the variables x and y. The data is as given…

Q: 1. If Jis any subinterval of [a, b] and if ø,(x) := 1 for x E J and 4,(x) := 0 elsewhere on [a, b],…

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Q: Example 3.8. For r = 1, 2, 3 and y = 1,2, let the joint pmf of X and Y be defined by x+ y fx,y(x, y)…

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Q: Find fy and f, and evaluate each at the given point. (x, y, 2) = x²y³ + 2xyz – 6yz, (-2, 1, 2) ,(X,…

A: Given :- f(x, y, z) = x2 y3 +2xyz-6yz  To find:- fx(x, y, z) fy(x, y,z)  fz (x, y, z)  fx(-2,1,2)…

Q: 22. (a) Prove that [0, x] = [0, y] for all x, y E Z, x + 0, y # 0. (b) Prove that [ax, ay] = [x, y]…

A: (a) we have to prove that  0, x = 0, y for all x, y∈Z, x≠ 0, y≠0 proof as x, y∈Z, x≠ 0, y≠0 Z is the…

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Q: 2D grai (a) Determine the domain and range of the given functions. Then sketch the f(x) = Vc2 – x²…

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Q: Prove that (X+Y) (X+Z) =X+YZ

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Q: {0, c, 5}. Let f (x) = x on [0, 5], and let P = Find two values of c in (0, 5) such that Uf (P) =…

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Q: Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies.…

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Q: 2.which of the ff.is the reverse process of chain rule?a additional rule b.product rule…

A: Reverse Process of Chain Rule:       The chain rule for derivatives allows to calculate the…

Q: > round (cov (DFRAME),2) M N M 2.71 -1.33 0.38 -1.20 0.78 N -1.33 2.89 -1.44 -0.89 0.38 -1.44 5.60…

A: A linear regression equation of Y on X can be expressed as : Y = a+ bX  where a and b are estimated…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.