Suppose the JPDF of X, Y is f(x,y)={1K(x2+y2)0

Q: Find all the local minima of the function f(x, y) = 15 x 2 x +3 y +6xy a) A local minimum occurs at…

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Q: Let us consider that (0,q^2 ), (1,1) and (p^2, 0) are co linear then prove that 1/p^2+1/q^2=1.

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Q: E. If T:(x, y) -→ (x + 2, y), then T²:(x, y) → (_²_, _?_).

A: Given: Tx,y→x+2, y To determine: T2x,y→?,?

Q: (b) 3x + 2 in Z,[x]

A: Given that 3x+2 in ℤ7x. We have to find all associates of 3x+2 in ℤ7x.

Q: (Q-3) function y=fG. This stretch bu a factor of 3 units. 1) Point (2-3) is a point 15 A gpint…

A: The given function is: y =  f(x) (2, -3) is a point on the given graph.

Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .

Q: If k >= 2 and x in R^ k prove that there exists y in R^ k such that y ne0 but xy = 0 Is this also…

A: If x has any components equal to 0, then y can be taken to have the corresponding components. equal…

Q: prove for all x,y in R^n: (1+||x+y||) ≥(1+||x||)/(1+||y||)

A: Sol:- The inequality to be proven is: (1 + ||x + y||) ≥ (1 + ||x||)/(1 + ||y||) Let's start by…

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: • The Doman of f(x) = 4-Vx is 1. (2, co) 2. [-2, c0) 3. [2, 0) 4. [-2,2]

A: The domain is the set of all values of x for which the value of function f(x) exists.   For f(x)=4-x…

Q: Find the Wronskian of a given set {yı, y2} of solutions of 7. (1 x2)y"-2xy' (a 1)y0, _

A: Consider the given equation.

Q: The product of sum (max term) form of the boolean function F = x +y'z is

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Q: 2) FIND THE INTERVAL OF CONV. * (x-1)^" 2 (n+i) n=0

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Q: Prove that if A is invertible, then 1 det (4) det (4-¹) = -

A: We have given that a square matrix A is invertible. To show that detA-1=1detA. We know that an…

Q: Suppose f(x, y, z) = xyz + 2xy + 2² · Compute the following values -(2,8₁16) - (-2,-8, 16) (1,-1,0)…

A: We have to find functional value.

Q: 2 -JM 3 0 5 Determine whether v is in the range of T. Fully justify your answer. 1 -2 -1 Let A = =…

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Q: 3 Compute the primitive of w= (z³ - x² z)dx ^dy - x²dx ^ dz + (3y² z - 3xz²)dy ^ dz

A: The primitive of a differential form is also known as its antiderivative. In this case, we want to…

Q: Compute Cov(X,Y)

A: Solution: From the given information, the joint distribution is

Q: * /Q1 = V4 – vx are: The domain D; and the range Rf of the function f (x) : D; = [0,16], R; = [0,2]…

A: Let's find given function domain and range.

Q: Prove that if AERnxm then rank(A) = rank(AT)

A: If A ∈ Rnxm then we have to prove that rank(A) = rank(AT)

Q: Find f such that the given conditins are satisfied.  f'(x)=5x^2-7x+4, f(0)=2

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Q: determine the singular points of the given function, type of these points and calculate their…

A: The given function is                                      f(z)=1z2-4z+13

Q: Let a be a real number and f(x, y) = 5ax?y+ 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

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Q: The psd of X(t) is given by [1+ @? for | @|<1 Sxx (@) otherwise Find the autocorrelation function.

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Q: +1²y=y² If the function u = ln (2¹+2²4 - v² ) then a Su rou + you is

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Q: Use the general chain rule to find DH (1,-1) given G(U)=G(u, v) = and H(U)= F(G(U)). /u²+3v² +2 F(X)…

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Q: Let the function ƒ : {1,2, 3,4, 5} {1,2,3, 4, 5} given by the following table. 1 2 3 4 5 f(x) | 4 1…

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Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: If l is a line through (0,0), the point (0,0) divides the line l into two rays. Also, a…

A: To determine for which rays starting at the origin ez is bounded, we need to analyze the behavior of…

Q: Prove that: (1+ x)*** (n+ 1)x C. + + 2 3 n+1

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Show that if F: AB and G, H F"" (GUH) = F"" (G) U f" (H) and F" (Gn H) = F²¹ (6) ^ F-1 (H) are…

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Q: a) f*(3) = b) f' (9) =

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Q: Show that u(x,t)= f((x+a*t)+f(x-a*t))/2

A: Given PDE is utt=a2uxx subject to ux,0=fxutx,0=0 We know that the general solution of the PDE is…