a) Let A = (-0, 5] cR, if R has the left ray topology. Find Āand Int(A). b) Let A = {1,2,3} CR, if R has the usual topology. Find Ext(A) and Bd(A). c) Let A = {1,2}cX = {1,2,3,4,5,}, if X has the cofinite topology. Find Ā, Int(A) and Bd(A).

Q: 1 2 Define an inner product on R² according to Let A -3 (u, v) Au · Av, where · denotes the usual…

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Q: H-w lo Find the dliscontinnity point of &cz): 4ca) = 5(2+i) 2+ci-2)Z-zi fcz) = c2) = Sin Z

A: Find the attachment

Q: p) Classify the following models as ARIMA(p,d,q). i) (1-B)x, = (1-0.3B),. ii) (1-0.5B+0.25B²)Vx, =…

A: ARIMA means auto regressive integrated moving average, It ia also written in the forn ARIMA(p,d,q)

Q: EX: Let S.[22] be asubset of IR Si-[-2-4J; S₂ = (-1,0]; S3 - (04]; S4= (1>2] {Si}, is a…

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Q: Evaluate (yzi+yj+zzk) - dA, where S is the boundary of the cube defined by -1<IS2,-1 SUS1, and 0<…

A: We can use gauss divergence theorem to evaluate the surface integral.

Q: 7. (a) V.(V4) = V²¢ (b) (4× R) _ (2-n).A n(A.R)R %3D E,r =|R|

A: a)

Q: Let S = Þ (D), where D = {(u, v) : u² + v² ≤ 1, u ≥ 0, v ≥ 0} and Þ (u, v) = (2u + 1, u − v, 3u +…

A: Let , where and . To Find:a) Surface integral.b)Double integral .

Q: 1. Check that each given function u is harmonic and if so then find a harmonic conjugate of u. Write…

A: Here as per our answering guidelines we are going to answer of red marked question (g) as follow:

Q: ON REDMI Y3 AL CAMERA - veifhy coucly's is Theorem for the function C) 3 Cosh(z+2 where C is the…

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Q: Explain why, no matter how the circuit is completed, Pip must place an even number of additional…

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Q: 5. Triangle JKL with verfices J(1,-1). K(2, 3), and L(3, -2): x=4 J': L': K'

A: In the question it is asked to take a mirror image of triangle ∆JKL about x=4. Coordinates of…

Q: (r,1) = (r sin (f), r– cos (1)), (r.1) = (5,-) s numbers in exact form. Use symbolic notation and…

A: In this question, the concept of the Jacobian of functions is applied. The Jacobian of Gr,t is…

Q: Let R be the annulus defined by {1 ≤ x² + y² ≤ 4} and let C₁ and C₂ be the circles of ratius 2 and 1…

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Q: Q. Let (X, B(R), µ) be a Borel measure space. If AnB=¢, BnC = 0, u(AnC) = 0. Determine µ(AUBUC).

A: Measure theory

Q: The equation +y= 9 in 3-space is cylinder Select one TrueO FalseO

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Q: Let X, Y subset U. Suppose that n(X)= 22, n(Y)= 20, and n(X intersect Y)= 16. How many elements are…

A: Let X,Y be subsets of U.  nX=22 , nY=20 and nX∩Y=16 It is given that nU=40. Find nX'∪Y:

Q: Let u = and v = Show that is in Span (u, v} for all x and y. y -1 5

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Q: / (sec. sec u tan u -1) du

A:

Q: Which of the following sets spans R? {(3,0,2),(0,0,0)} O {(3,0,-2),(5,1,0),(0,-1,1)} {(3,0,2)} None…

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Q: A S O Consi der Hhe folhning {(01), (-1,)}, B = [x]e - [;] %3D O find the fransi tion matria from B…

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Q: Show that (6.g) = (0,0) is unijomy continuous or not.

A: Uniform continuity

Q: Compute the Jacobian at the indicated point. G(r, t) = (r sin (t), r – cos (t)), (r, t) = ( 6,…

A: Jacobian of the function at a given point

Q: 2 22 2.2 り= ptasp;t P3 %3D 2

A: As per guidelines, we will solve only first question. Let us consider the vector space V3ℝ and…

Q: Lind dy/dx O ztanag In 3 Funas Inx I + Inx

A: Consider the provided question, We need to find  dydx of the given function. (1) Given,…

Q: Let V(F) be an inner product space and a, Be V. Show that a= B iff ( α, γ)- (β,)V γε V.

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Q: 4. Prove that: Jx'J,Ex) dx 2 3x J,Cx)-(x-3x) J.cx) -3

A: We find the value of the integration by apply the integration by parts and the recurrence relation.…

Q: Let C, be the rectangle with vertices (0,0). (1,0) (0,2) and (1,2) oriented counterclockwise. Find J…

A: Green's theorem problem....

Q: Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

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Q: Compute ,f for f(2) +6 + 6i, positively oriented. sin(32) and path 2 that is the boundary of the…

A: Let's see the method of integration. We use residue method to solve this integral.

Q: direct and direct let be a k. then pooduct of is z'G) product ZCH) and zck).

A: To show that Z(G) is a direct product of Z(H) and Z(K) when given that G is a direct product of H…

Q: Let P = {(z, y, 2) E R° | az + by + cz = 0} where (a, b, c) # (0,0,0). (a) Prove that (a, b, c) ¢ P.…

A: Given that P=x,y,z∈ℝ3 : ax+by+cz=0 where a,b,c≠0,0,0 (a) The objective is to prove that a,b,c∉P Let,…

Q: Q6A)If y = cos ¹) prove Zyy + z = 0.

A: See this solution in below

Q: Let F(x, y, 2) = (z, 1, y). a. Find divF and curlF.

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Q: 8.Prove the following relationships: a) I(X,Y)=H(X)-HOX/Y)

A: Solution

Q: HW) If rCH)=6 sinzt ċ+ Gcas zt j + 5tk find F,Ñ, V, a and speed at t-2

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Q: Prove the

A: Follow the steps that I listed given below pitcher.