Given a compact set A and a closed set B. ShOw that AB is compact!

Q: Let P = {0, 1/5, 2/5, 3/5,4/5, 1} be a partition of the interval [0, 1]. Let f(x) = x² + x + 1. Find…

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Q: 1. Evaluate the determinant of the matrix -3 4 P = 2-3 -4 -4 -3-4, -1 -2 3 1 -2 3 12

A: As per the guidelines I am answering only one question at a time. 1] P=12-34-1-23-41-23-412-3-4

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: 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: If A is nonsingular then det (adj(A)) = [det(A)]n-¹.

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Q: Let f(x)=e^(6x)-kx, for k>0 Using a calculator or computer, sketch the graph of f for k=1/9, 1/6,…

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Q: Let α be a zero of f (x) = x3 + x + 1 in some extension field of Z2.Find the other zeros of f (x) in…

A: If  α is a root of fx=x3+x+1, We need to find all roots of the polynomial fx=x3+x+1 in ℤ2α.

Q: (a) Please verify that = {1, cos x, cos 2x, ..., Cosmx, ..., an orthogonal set in a Hilbert space…

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Q: Use the shell method to write and evaluate the definite integral that represents the volume of the…

A: Given region is y+x=4, y=x, y=0. We have to find the volume of the solid by using the shell method.…

Q: Exercise (3) 1. Let 4 be a subset of normed space X. show that [4] is smallest closed subspace of X…

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

Q: f: A B be defined by f(x)= x-2 x-3 . Isfinvertible? Explain. .

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Q: Part A Ten granola bars and twelve bottles of water cost $23. Five granola bars and four bottles of…

A: Part A: Ten granola bars and twelve bottles of water cost $23. Five granola bars and four bottles of…

Q: 5. Let (α1,α2,...,ân) and (b1,b2,...,bn) be two n-tuples 1 1 bers and let p, q be two positive real…

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Q: Consider a conical tank that is completely filled with liquid. The liquid exits the tank from a…

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Q: (i)Suppose that g(x) = 1 + √x and f(g(x)) = 3+2√x+x, then find the function f(x) and (ii) let us…

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Q: An 8-lb weight stretches a spring 4 ft. The spring–mass system residesin a medium offering a…

A: Given: Weight stretches a spring is 8 lb. The spring–mass system resides in a medium offering…

Q: (ANB)U(ANC)

A: A∩B∪A∩C

Q: Suppose that α αnd b belong to GF(81)*, with |α| = 5 αnd |b| =16.Show thαt αb is a generαtor of…

A: Given : α, b∈GF81*We need to show that αb is a generαtor of GF81*.

Q: Suppose that f (x) and g(x) are irreducible over F and that deg f (x)and deg g(x) are relatively…

A: Given: Two polynomials f(x), and g(x) which are irreducible over F. deg(f(x)) and deg(g(x)) are…

Q: Question 7. Find the values of m for which the plane x + my = 2 intersects the elliptic paraboloid…

A: As per the question we are given the equation of a plane as : x + my = 2 and the equation of an…

Q: A half-pint container of vanilla costs $17.95.  What is the cost of 2 tsp.?

A: The relationship between pint and tsp(teaspoon) is   1 pint = 96 tsp.  Now,  half-pint  means  96/2…

Q: 7. By using operator methods find the general solution of the following system dy dx 2- + -y+x=2t +…

A: The given differential equations are 2dydt+dxdt−y+x=2t+1dydt−2dxdt+2y−x=2t These equations…

Q: a. At what point should the origin be shifted if the coordinates of a point (4, 5) become (-3, 9)?

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Q: Let D be a principal ideal domain. Show that every proper ideal ofD is contained in a maximal ideal…

A: Let D be the principal ideal domain. To show that every proper ideal of D is contained in maximal…

Q: With bases V1, V2, V3 andw1, w2, W3, suppose T(v1) = w2 and T(v2) = T(v3) = w1 + w3. T is a linear…

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Q: If P divides OA internally in the ratio ?\index{1}:?\index{2} and Q divides OA  extrnally in the…

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Determine the units in Z[i].

A: We have to find the units in Zi.

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 splitting field of x4 + 1 over Q.

A: Given: Let  E be the splitting field of x4+1over Q. To Find: Splitting field of x4+1over Q.

Q: Consider the differential equation x2y′′+3xy′+(1−x)y =0, x > 0.      ...... (11.5.38) Q. Obtain…

A: The given differential equation is x2y''+3xy'+1-xy=0, x>0 We have to find the Frobenius series…

Q: Ans. Y t 44. Y+tY' - Y = 0, Y(0) = 0, Y'(0) = 1. 45. tY"+(1-2t)Y' - 2Y = 0, Y(0) = 1, Y'(0) = 2.…

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Q: Quadrant sin # +6

A: Trignometry is defined as it is the measure of side and the measure of the angle of a triangle.…

Q: Describe the elements of Q(∛5).

A: We have to describe the elements of Q53.

Q: = √₂ + 2dX = 0 + 2* Vo 0.5 as = v₁ = (v₁³²) 8.89*107

A: We are given v12=0+2×7.9×1016×0.05 We have to find the value of v1

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: Show that x is not a generator of the cyclic group (Z3[x]/<x3 + 2x + 2>). 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: Title: Diamonds are forever... and costly! The table gives the price (in dollars) and weight (in…

A: Carat Price$ 0.50 4070 1.21 30,315 1.74 57,282 0.31 1404 1.51 45,928 1.04 24,679 1.20…

Q: Let A = R {3}, B = R - {1}, and let 1 x-2 Isfinvertible? Explain. x-3 f: A B be defined by f(x)=

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: find the general solution for      Z_xx+Z_x +x+y+1=0

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Q: Triple Integral A solid region E lies within the cylinder x² + z² = 1, above the plane y + z = 3 and…

A: As per the question we are given a 3d region E bounded within the cylinder x2 + z2 = 1 , above by…

Q: on metho partial pivoting, the following system of equations : x+y+z = 7,

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Q: Let ù be the set of natural numbers, S the set of square numbers, O, the set of odd numbers and E…

A: As per the question we are given the following four sets : U : set of all natural numbers S : set…

Q: Find xxx dj dr X+Y 2 x² + y²

A: Solution is given below:

Q: Let Show f is defined for all x > 0. Is f continuous on (0,∞)? How aboutdifferentiable?

A: Given: fx=1x-1x+1+1x+2-1x+3+1x+4-... To Show: Function is defined for all x>0 also explain…

Q: The is the ratio of the circumference of a circle to the diameter. Jacob Bernoulli, one of many…

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

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Q: Find the coordinates of the poin divides the line segments joining the points (6, (-4, 5) in the…

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Q: In a certain year, 13,081 professional train pushers are diagnosed with carpal tunnel.  The top…

A: 13,081 professional train pushers are diagnosed with carpal tunnel.  The top cities for such…

Q: If a is a group element, prove that every element in cl(a) has thesame order as a.

A: Given that, a is a group element. We have to prove that every element in cla has the same order as…

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…