Show by example that Σ(an/bn) may converge to something other than A/B even when A = gan, B = Σbn ≠ 0, and no bn equals 0.

Q: Example 2.30. Let X be a set and p the discrete metric. Then for every ECX, the set E has no…

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Q: 00 f(x) = Σχ* k=0 = 1 1 and S(x) = Ext. k=0 The remainder in truncating the power series after n…

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Q: 1. Evaluate the determinant of the matrix 2 -3 4 -2 3 -4 -2 3 -4 2 -3-4, P Show all your work. 1 -1…

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Q: ven P(B) = 0.38, P(A and B) = 0.26, P(A or B) = 0.45, what is P(A)? Answer in decimal form.  Round…

A: We are given PB=0.38PA∩B=0.26PA∪B=0.45PA=?

Q: A connected graph with 7 nodes and 7 edges has how many loops?

A: Given: The nodes of a connected graph=7 and the edges of a connected graph=7To find: The number of…

Q: irst part of the question is that convert the following Cartesian coordinates to the corresponding…

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Q: Find the equations of the tangent and normal to the equation: y (15-3x²)Inx when x = 1.

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Q: 2. Find the solution of Cauchy problem: (a) y lu, tuy = u, u(2,1) = ? (b) xux + yuy=x²-y, u(1,y) =…

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Q: Using the definitiOn Of a uniform cOntinOus sequence, prove the function uniformly continuous On…

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Q: Given P(A) = 0.37, P(A and B) = 0.14, P(A or B) = 0.58, what is P(B)?

A: We have given that                P(A)=0.37 , P(A∩B)=0.14  and P(A∪B)=0.58Since we know that…

Q: nd the smallest positive root of the equation x^4 - 3x^3 + 2x^2 + 2x - 7by nebyshew method of third…

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Q: Let {w1,w2, . . . ,wn} be a basis of the finite dimensional vector space V. Let v be any non zero…

A: w1,w2,...,wn is a basis of the finite dimensional vector space.

Q: For a commutative ring with unity we may define associates, irreducibles,and primes exactly as we…

A: Given: Z12=0, 1, 2, . . . , 10, 11. To show: Both 2 and 3 are prime in Z12 but 2 is irreducible and…

Q: When people talk about "dynamic programming," what do they mean, and how does it really work?

A: Dynamic programming is a mathematical optimization technique that involves breaking down a complex…

Q: Find the splitting field x4 - x2 - 2 over Z3.

A: In mathematics, a splitting field is a field extension that contains all of the roots of a given…

Q: p = 39 is not prime. Find a number a that has no inverse z ( mod 39). This means that az = 1 (mod…

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Q: Let C be the curve y = 5x³ for 0 ≤ x ≤ 2.2. sat

A: Given C be the curve y=5x3 for 0≤x≤2.2.               To find the surface area of the revolution of…

Q: he equation of a clove ret :0 a given sustem of axes is 3X^2+2xy+3y^2=10 ind its equation if the…

A: With the given notation , we have    x=x'cos45-y'sin45=x'-y'2and  y=x'sin45+y'cos45=x'+y'2

Q: The demand function of a monopolist's product is p = √600 – 2q. a. How many units should be produced…

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Q: a a² Xn+1 = pxn+q¬+r- 5 x₁

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Q: 4. Consider a relation R on X={a,b,c}. R= {(a,a), (b,b), (b,c), (c,b)} Please determine whether R is…

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Q: Consider the second-order system: dx₁ dt = -ax₁, dx2 dt = -bx₁ - Cx₂ where a, b, c > 0. What can you…

A: Gven that :Consider the second order system:dx1dt=-ax1dx2dt=-bx1-cx2where , a,b,c >0.

Q: irst part of question is that Find the locus of a point such that the sum of its distance from the…

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Q: Let f: IR be a convex fun Theorem x1,x2,.. , are points in I and A₁, A2,..., An are real numbers [0,…

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Q: W = -e-³x; W₁ = −e-²x(4+ ex)-¹; W₂ = ex(4+ ex)-¹ want to find functions u₁(x) and u₂(x) such that yp…

A: We have  u1'=-e-2x4+ex-1-e-3xandu2'=-e-x4+ex-1-e-3x Lets simplify it

Q: Find the rank of A. The rank is not the dimension of the whole output space W. It is…

A: Given that, Find the rank of A. The rank is not the dimension of the whole output space W. It is…

Q: Given P(A) = 0.86, P(B) = 0.08, and the fact that events A and B are independent, What is P(A and…

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Q: Describe all possible ways in which two planes (passing R3 could intersect. Suppose V is a vector…

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Q: A reflecting telescope has a parabolic mirror for which the distance from the vertex to the focus is…

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Q: KIN x≥1 0 x < 1 f(x) = {2 lim f(x) Show x→1 there isn't any.

A: fx=x2,x≥10x&lt;0

Q: AB is a variable line sliding between the coordinate axes in such a way that A lies the x-axis and B…

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Q: Develop a model using the Analytic Solver Platform that will determine how many 130-inch rolls to…

A: The company makes standard 130- inch- wide rolls of thin sheet metal and slit them into smaller…

Q: 2. Let A and B be arbitrary 3 × 3 matrices. State "True" or "False" for each of the following…

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Q: Prove if the ff. arguments are valid using any formal proof of validity. j→ k jV (kV ~l) ~k 2.…

A: Valid Argument:  If given argument is Tautology then that argument is Valid.

Q: 24. 2 -3 4 T -3 20 0 2

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Q: So, what does "dynamic programming" really entail?

A: Dynamic programming is a mathematical optimization method and a computer programming method.

Q: Show that x is not a generator of the cyclic group (Z3[x]/&lt;x3 + 2x + 2&gt;). Find one such…

A: The given cyclic group is: Z3x/x3+2x+2*. We have to show that x is not the generator of the given…

Q: Determine what functions of time will appear in y(t). Which y(t) are oscillatory? Which have a…

A: The given function Ys=2ss2+4s+8. We have to find the function yt, and yt are oscillatory, and a…

Q: Determine a Green function for the equation x²y"(x) + 2xy'(x)-2y(x) = f(x), with boundary conditions…

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Q: Find the general solution of the following ODE "motion of the harmonic oscillator". Show that this…

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Q: Two points (0,0) and A(3, √3) with another point P from an equilateral triangle . Find the co…

A: Part A

Q: Find the splitting field ofx4 + x2 + 1 =  (x2 + x + 1)(x2 - x + 1)over Q.

A: Given: x4+x2+1=x2+x+1x2-x+1To find: The splitting field of x4+x2+1=x2+x+1x2-x+1 over Q.

Q: The 3 by 3 min-or matrix that reflects through the plane n T v = 0 is M = I -2nn T. Find the…

A: As per the question we are given the plane fx + h + ½z = 0 and we have to find the reflection of the…

Q: Apply the method of undetermined coefficients to find a particular solution of each of the following…

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Q: Determine the units in Z[i].

A: We have to find the units in Zi.

Q: The curve y = sqrt ( 4 - x sq. )  ,-1 &lt; = x &lt; = 1  , is an arc of the circle x sq. +  y sq. =…

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Q: Prove that a group of order 105 contains a subgroup of order 35

A: To Prove: A group of order 105 contains a subgroup of order 35.

Q: nsider the following function: a) Find: 1) 01 2014 3) a2f ахду a2f дудх 5)011 = 4) b) Solve aly ola…

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Q: Let F = Z2 and let f (x) = x3 + x + 1 ∈ F[x]. Suppose that a is azero of f (x) in some extension of…

A: Given: F=ℤ2 and a is a zero of the polynomial fx=x3+x+1. We have to: (i) Find number of elements in…

Q: Let α be a zero of x3 + x2 + 1 in some extension field of Z2. Solve the equation (α + 1) x + α = α2…

A: Given that α be a zero of x3+x2+1 in some extension field of ℤ2. We have to solve the equation…