Use the definition of compactness to prove that a closed subset Y of a compact set XCR is compact.

Q: wire have. To Find gradient if possible, is a ние в (х,уі) іsa possible to чому в (x,y,z) = 40%,…

A: We have     We have to find the gradient if possible,Here f(x,y,z) is a scalar function hence it is…

Q: 2. Find the solution set of the following equations (3-2x)-¹ (d) x-1 (e) (x-7)x¹ + (x-¹-7)x=0. + x…

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Q: for boundary is 1/n^2 or 1/n^2 U 0 ?

A: Boundary point : the boundary of a set A is the set of all elements x of R (in this case) such that…

Q: Use index notation to show that: If V-u-0,V-v=0, and Vxw=0, then V-[(xv)xw]=w[(V)-(LV)v]

A: Given  .To prove  .The formula for cross product is given by .

Q: Suppose the sequence {sn} is bounded above by M and {sn} converges to M. Prove sup{sn : n € N} = M.

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Q: 2. Consider the second-order differential equation d²x dx +a + b²x = 0 (a, b positive real…

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Q: ● Let u = 2-25 - 2k + ● and = 2î - 2Ĵ+k. Find a vector w such that the parallelepiped spanned by u,…

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Q: 1. Z₁ = 1-5i 2. Z₂ = 3 + 2i Z2 3. Z3 = −7+i

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Concerning the polynomial p(x) = ao+a₁x + +anx", prove the following result. For a given x, we set…

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Q: Let x € Z. Prove that if 2 | (x²-5) then 4 | (x²-5).

A: Given that .The objective, if then prove that .

Q: Given the integral domain ≺D,+,⋅≻ and k,l,m∈D, with m≠0. Then mk=ml⟹k=l.   True False

A: (.)  In an integral domain  product of two non - zero elements is non - zero.i.e.  if  such that

Q: Find the general solution of the system x'(t) = Ax(t) for the given matrix A. A = -1 1 0 1 4 1 0 131…

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Q: Candidates A, B, C, and D are competing to win an award. There are 5 voters in this election. The…

A: We have to find the candidate who would win using plurality method when is dropped.

Q: Consider the parametric equation x = 2 cost, y sin t 9 z = 1². (a) Describe the curve in 3…

A: We shall use MATLAB to plot the curve in 3d.1t = linspace(0, 4 * pi, 1000); % Adjust the range as…

Q: 3. Let T: R³ R³ be a linear transformation. We know What is T 0 ¹-B ·®-W O-H = [] T 4 T = = 0 6 8…

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Q: The divergence of the vector function G(x, y, z) is given by div. G D.G C where, V = 2n + 3y on + ka…

A: The divergence of the vector function  is given by  where, .The rotational of the function  is…

Q: Let A = a. Find A 1 2 7 16 b₁ = -1 7) 1 b₂ = 6 b3 - 2 - 20 and b4 = 0 - 12 1 and use it solve the…

A: The objective is to solve the system.

Q: Q1. Each of the two tanks contains 200 gal of water, in which initially 100 lb (Tank T₁ )and 200 lb…

A: Given Information:Total capacity: 200 gal of water on each tank.Initially, tank 1 contains 100 lb…

Q: Below are several induction hypothesis statements. Select all the statements that are using STRONG…

A: Strong Induction: In strong induction, we assume that the statement is true for all  we prove the…

Q: Graph the following function (using a graphing calculator or desmos.com). Use the approximate…

A: We have given functionWe have to draw the graph using calculator and approximate the relative…

Q: find the principal value of (3-3i)^3i

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Q: 2. Consider the matrix A = 40-1 03 0 10 2 . (a) Find the eigenvalues of A. (b) Find a basis for the…

A: Let us find the eigenvalues and eigenvectors.

Q: I and B₁ = B10 = 0 B-{[12] [3 8. (a) What is PB₁←B₂? (b) Assume [v] B₂ = (c) What is v? 21 1 (3) G "…

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Q: Q.No.4.a. When problem become unrestricted after changing primal to dual simplex Method justify your…

A: Given information:Minz=x1−3x2+3x3Subjectto:3x1−x2+2x3≤72x1+4x2≥−12−4x1+3x2+8x3≤10x1,x2,x3≥0To find:…

Q: Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.…

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Q: Fill in the first 3 levels of Richardson extrapolation to estimate the derivative of sin(a) at a =…

A: Given information:Given function: f(x)=sin(x)Point of interest: x=0.5Initial step size: h0​=0.8To…

Q: Evaluate the following limit. 4y² - 196 lim (x,y) →(7,7) xy-7x Select the correct choice and, if…

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Q: Use the simplex method to solve the linear programming problem. Maximize subject to: with z = 3x₁ +…

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Q: Consider a simple graph G with 7 vertices labeled A through G. Suppose that every vertex is…

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Q: Show that if a, b, c ER then: (a) a−b=-(b-a). (b) (a + b)(ab) - a(a - b) + b(b-a) = 0. (c) a b=0⇒a=0…

A: To prove Hence proved.

Q: Find the inverse Laplace transform, f(t) of the function F(s) f(t) = ,t> 0 = 4 s+2 S V -2

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Q: Given: f(x) = 5sinx for -2pi <x<-pi/2 = 4 for x=-pi/2 =x^2 for-pi/2<x<2 =8cosx for 2 < x <pi =4x for…

A: Given F(x) = 5 sin x for -2π &lt;= x &lt; -π/2 = 4 for x= -π/2 = x^2 for -π/2 &lt; x&lt; 2 = 8 cosx…

Q: The parallelogram determined by non-zero vectors 7 and w has the same area as the parallelogram…

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Q: 5. Show that: b>0 and a <0 such that a² = b⇒a= -√b. 6. Prove that there are real numbers a and b,…

A: We are given that b&gt;0 and a&lt;0Now, let a2 = b    Taking square root on both sides, we get,…

Q: Give examples of two sets A and B such that An P(A) = B and P(A) ≤ AUB.

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Q: Mark the following either true or false. Justification is required. (a) The dimensions of Col A and…

A: To answer the questions we can use following formula(a) For a matrix A with order m × n, Rank (A) +…

Q: d. cot(x) - csc(x) = sin(x) cos(x)-sin(x) sin²(x)

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Q: Let A and B be rings. Define addition and multiplication on the Cartesian product A x B by (x,y) +…

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Q: Math

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Q: Consider the following DAG: A) B G D C E F

A: Topological Sort: In a directed acyclic graph (DAG), a topological sort is a linear ordering of its…

Q: For n € N, let A₂ = (–½, 2 − ¹). Determine UnEN An and nen An.

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Q: Let f and g be continuous functions from R to R. Show that the function F(x) = min{f(x), g(x)}  is…

A: We have to show F(x) = min{f(x), g(x)} is a continuous function when f and g are continuous…

Q: Let = (2,-1, 1) and b = (1, 1, 2). Find the area of the parallelogram determined by ✯ and 7. Find ||…

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Q: 5. If limn→∞ an 1 (a) limn→∞ bn (b) limn→∞ A and limno bn = B 0, prove B' an = bn B.

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Q: A Consider the following DAG: L B G D C LL F E Give an example of a topological sort, a maximal…

A: Let us define the definitions one by one......................Topological Sort:The topological sort…

Q: The image below shows the graph of the function f(x). On the same image, sketch the graph of f'(x).…

A: The graph of the function  is given.sketch the graph of the derivative  as follows.Let us consider…

Q: Find the first three non-zero terms in the Laurent series expansion of the function f(z) =1/(z^2 +…

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Q: From the question above predict the worldwide sales of e-cigarettes in 2012. Use the average growth…

A: From the question above predict the worldwide sales of e-cigarettes in 2012. Use the average growth…

Q: An elliptic curve is a curve of the form y^2 = x^3 + ax + b for some constants a, b. These curves…

A: Given information:An elliptic curve is represented by the equation y2=x3+ax+b, where a and b are…

Q: your initial discussion post, reflect on the activity by answering the following questions: How can…

A: An absolute value expression that is greater than a value is considered an OR statement because it…