i). Find the highest normal form of a relation R(A,B,C,D,E) with FD set as (BC->D, AC->BE, B->E}

Q: Let L be the line in R2 through the points [:] } Find a linear functional f and a real number d such…

A: First, we will find the equation of a line given two points.

Q: Determine whether the given set of functions is linearly independent or linearly dependent on the…

A: Let f and g be differentiable on [a, b]. If Wronskian W(f, g)(t) is nonzero for some t in [a, b]…

Q: Show that if f , g, and h are differentiable, then                                          [f…

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Q: Assume that f is an odd function defined on R and t e Rt. Compute

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Q: Construct a linear map L(z)=az+b that will send the imaginary y-axis to the line v=-u.

A: we have to constract a linear map that maps the y-axis to the line v=-u Basically we have to…

Q: Consider the closed curve C, which is th

A: Given, the closed curve C, which is the image of the path…

Q: 4) B. Let A = {u, v, w}, B = {x, y, z}. Determine whether the relation R = {(u, x), (v, z), (w, y)}…

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Q: Determine whether the work done along the path C is positive, negative, or zero. zero O negative O…

A: We know,       work = ∫cF.dr               = ∫c∥F∥∥dr∥ cosθ    where θ is angle between F and drIf…

Q: (a) Prove the following relation: B(x + 1, y): B(x,y) x + y %3D

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Q: If F = x? a, – xz a, – y?a,, evaluate f F - dl around the path shown in the diagram

A: Given function is, F=x2ax^-xzay^-y2az^ Then by using Stokes's theorem we have to calculate ∮F·dl→…

Q: Find all the saddle points of the function. f(x.y)=xsin O (5 m, 0) O (5 Tom, 1) 이름이 O (0,5 m) 1/5

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Q: (5) Find the most general function f(t) so that the curve F(t) =, shall lie in a plane.

A: The most general function for f(t) is a constant function, f(t) = c:   <a cost, a sint, c>

Q: With X a topological space, is the function defined as A:X →X × X,x → (x, x) continuous? Investigate

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Q: t, 0<t<1 f(t) -1, 1, 1<t< 2 || –t, 2<t<10

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Q: Let A(x) = f(t) dt for f(x) in the following figure.

A: GivenA(x)=∫0xf(t)dtAnd the graph of f(x)

Q: Let f(x, y) = xy - 4x on

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Q: Find a function r(t) that describes the line segment from P(2,7,3) to Q(3,1,1). O A. r(t) = (2 – t,…

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Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

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Q: Define a relation M from R to R as follows: For all real numbers x and y, (x, y) E M means that y =…

A: Use the vertical line test; if you can draw a vertical line anywhere that crosses more than one…

Q: Consider the following consumer function: соnsumption, В, + Bzlncome, + u, uz = Income, Vi v ~ (0,…

A: Reviewing the information, given, consumptiont=β1+β2 Incomet +utwhere,ut=Incomet νtνt~0,σ2

Q: Define a relation T from R to R as follows.for all real numbers X and Y, (X,Y)€T means that Y2-X2=1…

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

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Q: Suppose that S = {v} is a linearly dependent set. What is v?

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Q: 2t , 0<t < 2 f(t) = lo, 2<t<10

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Q: Is the set X is linearly dependent or independent X = {(1,0,1,0), (0,3,0,1), (1,1,2,2), (3,4,1, −2)}

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Q: Let A = {x, y} and B = {w,z}. Describe all relations from A to B. Indicate which of these are…

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Q: Let F(x, y) = (x, 0). Prove that if C is any path from (a, b) to (c, d), then F dr = 3 – a²)

A: Consider the provided information, Let Fx,y=x,0. Prove that if C is any path from a,b to c,d then…

Q: A shop sells 3 brands of textile: B,, B,, and B, of yarn, each of which is a blend of Orange (0),…

A:

Q: (a) Prove the following relation: В (x + 1,у): B(x, y) x +y %3D

A: We have give Beta function relation, we have to show left hand side is equal to right hand side.

Q: Let X have the property that every pair of disjoint closed sets can be separated by a continuous…

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Q: show that F(X<1|Y<y) + P(X <1) for some z, y.

A: dependent events:  Two or more events are said to be dependent if occurrence of one affects the…

Q: Eliminate Band a for the relation. x=Bcos(wt+a) in which w is a parameter. *

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Q: Is the cobb-douglas function strictly concave when a1 +a2 <1 when

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Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: Let f(x, y, λ) = xy + λ(5 - x - y). Find f(1, 2, 3).

A: Given : fx,y,λ = xy + λ5 -x -y

Q: Let f(x) = vV72 – x and g(x) = x² – x. Give the domain of f o gusing interval notation.

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Q: Let A = {u, v, w}, B = {x, y, z}. Determine whether the relation R = {(u, x), (v, z), (w, y)} from A…

A: In R from A to B is an injection function as well as a surjection function.

Q: Is defined for some value of s?

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Q: Determine whether the work done along the path C is positive, negative, or zero. c/

A: we know that Work W=∫C F→·dr→

Q: Let f(x)=x in(x). Find the interval on whichfis increasing. (a) (0, o) (b) [e¯ !, ∞) (c) [1, ¤) (d)…

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Q: Determine whether the work done along the path C is positive, negative, or zero. Ozero negative…

A: To determine whether the work done along the path C is positive , negative or zero .

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

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Q: Let L be the line in R2 through the points [:][] and Find a linear functional fand a real number d…

A:

Q: Let f(x, y, z) = x2 (e)^y/z. Compute f(-1, 0, 1), f(1, 3, 3), andf(5, -2, 2).

A: Let fx,y,z=x2eyz 1. we have to compute f(-1,0,1) as, fx,y,z=x2eyzHere x=-1, y=0,z=1f-1,0,1=-12e01=1…

Q: Given an example of a linear map T: R4 → Rª such that range T = null T (or equivalently range T =…

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Q: Determine whether the work done along the path C is positive, negative, or zero. /c/ zero negative…

A: For calculating the work done from the field we will have to see the direction of both vector field…

Q: Suppose f : [a,b] → R is a continuous function. Prove that the direct image f([a,b]) is a closed and…

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Q: Let T : R? →→ R² and S : R² → R² be a linear maps such that r() - (1) (G) = (;) TO and S(( 2 1 Then…

A: Given: T: R2→R2 ,  S: R2→R2 be linear maps such that T10=11 &amp; S11=12 To determine: S∘T10

Q: Let a, b, c and d be four approximations of the fixed point p of function f such that a – f(a) : =…

A: Minimum absolute difference is best approximation  so B is correct

Q: Let X and Y be two discrete spaces, then *

A: Note: Since you have posted multiple questions we are only allowed to solve the first one. Thankyou…