Limit Comparison Test (a). Suppose that E ak and Ebk are series with positive terms. If ak lim = c, 0

Q: Prove that T is the discrete topology for X iff every point in X is an open set

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Q: Find all the arymptotes of the cubic polynomial ー24y.C2nーツ)+yメーソ)o: aned show thaf Cut the cunne in…

A: Given function is x3-2y3+xy(2x-y)+y(x-y)+1=0 There is no asymptotes parallel to x-axis and y-axis…

Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Laplace transferom of the function

Q: Evaluate the double integral over the rectangular region / 4(r sin (2) – y sin(x)) dA; R = {(x, y) :…

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A: Given E=-2x2yi^-2xy2j^+2xy2zk^ where 0≤x≤2, 0≤y≤1, 0≤z≤1

Q: Consider this Preference Voting Table from 50 voters and 4 candidates Rank / Number of 19 14 10 7.…

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Q: A voter who has a weight that is greater than or equal to the quota is called a dictator. In a…

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A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 4. Is the graph below bipartite? If so, list the vertices in the one part and the vertices in the…

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Q: Which of the following is a three-point geometry? 3.1

A: Which of the following is a three point geometry :-

Q: Solve (D4 + 2D² + 1)y x cosx +3*

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Q: Which of the following is four-point geometry?

A: Axioms of Four Point geometry is given as 1.   There are exactly four distinct points 2.   Any two…

Q: Let : IR > IR be a canvex (ontinous uith contont L.' For a hx os follou s. fundion and vf is…

A: As per the question we are given a multivariate convex function f(x) whose gradient ∇f is Lipschitz…

Q: Evaluate using Laplace Transform: f(t) = | tcos3 3t dt e-4t

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

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Q: Verify F(1,1; 2; x) = -x¯ln(1 – x) By expanding each function in a power series about x = 0.

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Q: For the subspace below, (a) find a basis for the subspace, and (b) state the dimension. {(a, b, c,…

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Q: Find the L.T 1 for the following function 2S F(S) = 52 - S- 6

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Q: 3. Write down the name of the conic given by the polar curve r = 6/ (2 - sine). Determine the…

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Q: 2 The half range cosine expansion of f(t) = t +t, 0<t<1 is 5 f(t) 2 2 + [2(3(– 1)" –1)] cos…

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Q: (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1),

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Q: The integral TT tan x sec?x dx 2 O none of them is an impróper integral of type I that diverges is…

A: Improper integral

Q: 8. Interval -c<x< c; function, f(x) = ex

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Q: For each of the following series determine if the series converges or diverges. In(n) n n=2 n3 n=0…

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Q: Determine the volume of the solid obtained by rotating the region bounded by y=x^2-4x+5,x=4 , and…

A: volume of the solid of revolution about x axis of a curve y=fx, from x = a to x = b is given by…

Q: Using determinants, find area of each: A. (1,4) (10,2) (8,12) B. (1,-9)(6,-3)(-3,1)(-5,-6) C.…

A: The given problem is related with area of quadrilateral. We have to find the area of the following…

Q: 2. f(t) = V1+ sint + (7t)4 + sin 2t %3D

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Q: The complex number z is defined by z= 3 -z+4.j where z is real. a) Find, in terms of z, the real and…

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Q: Let W- ((x. y, 2)|x-2y 32) Vector addition and scalar multiplication are defined by (x, y.z) + (u,…

A: Note: " As per our guidelines we will solve only first question . If you want any specific question…

Q: edge? 3. What will it cost to tile a kitchen floor that is 12 feet wide by 20 feet long if the tile…

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Q: Find the Laplace transform of: 1. f(t) = e-3t) sin(2t) cos(3t) cosh(t)

A: Laplace transferom of the function

Q: YPLEDIS Company wants to mix exactly 600 pounds of a special kind of dog food; There are two…

A: Let  x1: amount of protein P1x2: Amount of protein P2 the objective is to minimize the cost…

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Q: Evaluate using Laplace Transform, find a: sin(t + a) cos(t + a) f(t) = | 3 dt 8. e2t

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Q: Given that r 1.0 1.2 1.4 1.6 1.8 2.0 2.2 y 2.7183 3.3201 | 4.0552 4.9530 6.0496 7.3891 | 9.0250…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Find the solution of the equation cos y dy? which tends to zero as i → 0o and has the value cos y…

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Q: 5s+3 6s F(s) = (5s2+4s+1) -- 9 s2 +7

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Q: 24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1)2, 1)-1 1:

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Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

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Q: Choose two figures which are topologically equivalent to each other 20 L.

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Q: The complex number z is defined by z = 3·z + 4.j where z is real. a) Find, in terms of z, the real…

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Q: 3. (a) The trapezium rule for integrating a function over the interval [-h, h] can be written in the…

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Q: 30. The altitude of a right circular cylinder is twice the radius of the base. The altitude is…

A: Given that the altitude of a right circular cone is twice the radius of the base, i.e.  h=2r…

Q: Solve the given ODE using Laplace Transform 1. y" – 4y' + 3y = 6t – 8 ; y(0) = 0,y'(0) = 0 %3D

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Q: Evaluate the triple integral. /I | ry sin(yz) dV, where G is the rectangular box defined by the…

A: We need to evaluate ∫∫∫Gxy sinyz dV 0≤x≤π  , 0≤y≤9,  0≤z≤π54 So, we need to find ∫09∫0π54∫0πxy sinyz…

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Q: Evaluate using Laplace Transform: tsin3 3t dt e-3t 00 f(t) ||

A: We have to apply the Laplace transform method.

Q: The integral TT tan x sec2x dx O none of them is an impróper integral of type I that diverges is an…

A: Solution

Q: Choose two figures which are topologically equivalent to each other L 20

A: See answer below

Q: The complex number z is defined by 3.z + 4·j where z is real. a) Find, in terms of æ, the real and…

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