How can I show that the collection  A composed of empty set and all cofinite subsets of X Is a  sets whose complement is finite, form a topology on X. Can I  call it the cofinite topology of X? Will the cofinite topology be  Hausdorf?

Q: 6. Does the sequence converge or diverge? If it converges, then find the limit. an- nª-3e" 2e" + nª

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Q: Exercise 8.2.4 Find the characteristic polynomial, eigenvalues, and basic eigenvectors of the matrix…

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Q: The growth of a certain population (in millions) over time, P(t), is modelled by the differential…

A: The population will grow if 0 \)" data-mce-style="cursor: default;">dPdt>0.The population…

Q: Let D be the circle |z| = 3, oriented counterclockwise. For any positive integer n compute the…

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Q: Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of…

A: The axis of symmetry for an upward/downward parabola with vertex (h,k) is x=h.The axis of symmetry…

Q: 2л • St* S* sin(2) dy dx R 0 Let Rho the region shown below. Find the 3. Evaluate 1

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Q: Problem 2. (a) Let 7₁,..., Um be vectors in R" such that: v; ‡ Ō, for all i = 1, ..., m, and ● Vi v…

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Q: (b) For subspaces X and Y, the sum X + Y is a direct sum (denoted X + Y) if every VEX + Y can be…

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Q: 3. Let f, g to be two continuous functions on [a, b] and f(a) ≥ g(a), f(b) ≤ g(b). Prove that Exo €…

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Q: Find y'(0) and y"(0) from the following table ofvalues: X 0 1 2 y 4 8 15 3 4 7 6 5 2

A: From the given table upper digits are values of X and lower digits are values of Y(X).

Q: 11. TRUE or FALSE. Identify if the statement is true or false. If True, then prove or explain. If it…

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Q: Calculate the triple integral J₁ (2² + y³e²²) dxdydz, where R is the parallelepiped R = {0≤x≤ 2,1 ≤…

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Q: d²y_1 dy _ 4x²y = 0, -∞ < x < 0, y₁ = e²² dx² x dx

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Q: If (x, y) and (X, Y) are the coordinates of the same point referred to two sets of rectangular axes…

A: and are the co-ordinates of the same point referred to the set of rectangular axes with same origin.

Q: Que 11: The characteristic of a finite field is necessarily non-zero but the converse is not true.

A: Our claim is that the characteristic of a finite field is necessarily non- zero but the converse is…

Q: Suppose an RL circuit with a 110 resistor and a 6H inductor is driven by the voltage 5t E(t) = eſt…

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Q: Let Z= (-1,2,2) be a point in R³. Find the closest point to Z that lies on the plane given by…

A: We have to find the closest point of  that lie on the plane

Q: Compute 2 -2 5 2 To enter your answer, click in the answer box. Then choose the "Matrix" tab and…

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Q: Suppose ƒ : R² →→ R is a function and f(x, y) = 42 defines one of its level curves. A new insect, a…

A: we have given the level curve f(x,y)=42.When a bug is walking on this level curve, the bug feels hot…

Q: The Boeing Company faces a critical strategic choice in its competition with Airbus Industries for…

A: The Boeing Company faces a critical strategic choice in its competition with Airbus Industries for…

Q: Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation of…

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Q: Use quadratic regression to find a model for this data. Round your coefficients to the nearest…

A: Using quadratic regression we have to model the given data

Q: 25.000 0.02 (1+ 1 + . 0.02 48 12 0.02 46-1 12

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Q: Compute the determinant by cofactor expansion. At each step, choose a row or column that involves…

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Q: Use Stokes' Theorem to evaluate [ F. dr where F = (x + 10z)i + (7x+y)j + (4y − 2) k and C is the…

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Q: k The electrical resistance R of a certain wire is given by R = where k is a constant and r is the…

A: Electric resistance of a certain wire is given by  where  is constant and  is the radius

Q: Part A Prove the following theorem using either regular or strong induction. Theorem: Suppose that n…

A: We shall prove this problem using regular induction

Q: For the linear programming problem to the right, (a) Set up the simplex tableau. (b) Determine the…

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Q: E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line…

A: Given that C1 is the curve parameterized by r(t)=(cos2⁡t,sin⁡t),t∈[−π2,π2].Let C2 be the line…

Q: Find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace? 1…

A: (.) Subspace spanned by the vectors,        (.) Basis : Basis of a vector space is a linearly…

Q: Use the Trapezoidal, Midpoint, and Simpson's Rules to approximate the integral 9 In(x) 2 + x S₁ dx…

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Q: roblem #10: Find the flux of F(x, y, z) = yi - xj + 6k across S, where S is the helicoid with vector…

A: In this question, we will find the flux.

Q: Digicel and Flow operate on the island of Carriacou, Grenada. Digicel staff’s tenure is said to be…

A: Given information:Flow's Staff:Gio has worked for x years.Nakita worked for 8 years longer than…

Q: Use properties of determinants to evaluate the given determinant by inspection. 0200 -5000 0006 0 0…

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Q: Determine if the following functions are homomorphisms / embeddings / isomorphisms. You must only…

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Q: please answer c) e)

A: For the part (f), mention which diagram expert has to draw.

Q: Exercise 8.1.6 Suppose A is a 3 x 3-matrix with eigenvalues 21 = 1, 22=0, and 23=2 and corresponding…

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Q: : {1+x,1 − x²,1+x+ x² } and B' = {2 − x, 1 − x+x²,3+2x}. 3.) Find the transition matrix from B to…

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Q: (c) Prove that there are infinitely many prime numbers.

A: Assume there are finitely many prime numbers. Then, we can say that there are n prime numbers, and…

Q: Let A be a subset of the real numbers. A number s is called a least upper bound for the set A…

A: Since you have posted a multi subparts question according to guidelines I will solve first(a,b,c)…

Q: ) Using either Prim's or Kruskal's algorithms, determine the cost of the minimum spannin tree which…

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Q: FOR PART C, can you explain how they got the quadratic equation

A: The growth of a population over time P(t) is modeled by the differential equation .To Find:Explain…

Q: Evaluate the Improper Integral using LIMITS. If convergent find the exact value. I fx² Inx dx 0

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Q: why 4?

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Q: verify stokes` theorem for a vector function F = yi + zj + xk on the surface S (the paraboloid) z =…

A: The given vector field is  on the surface (the paraboloid)  .To verify the Stoke's theorem.Consider…

Q: 2. Let G be a group. Recall we showed in class that if |G| is finite, then o(g) is finite for all g…

A: be a group.If  is finite then  is also finite where We have to show the converse of the statement…

Q: Prove there is no real number a such that 28 + x6 + 1 = 2x³

A: The given equation .The aim is to prove the equation has no real solutions.

Q: The given T is a linear transformation from R2 into R². Show that T is invertible and find a formula…

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Q: lim, 3n+1 3 1/5 7n-3 7

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Q: (b) Show that the sequence defined by a₁ = 3 and for n > 1, an = √3+an-1 converges. Find the limit.…

A: Given sequence is a1 = 3 and for n &gt; 1, an = √(3+an-1).