Does the limit   limx→0+ sin(1/x) exist? Justify your answer.

Q: Prove B = {ne N} U {0} is compact.

A: Heine Borel Theorem:     Every Closed and Bounded Subset of R is Compact.So to prove the  above set…

Q: Suppose the Texas Department of Motor Vehicles is tracking the number of car, truck and motorcycle…

A: The MATLAB variable that defines the total number of crashes for the years 2000 to 2009 (all…

Q: Sketch a directional field for the equation. Identify at least 4 isoclines. dy dx = y +x Isoclines:

A: This is a problem of directional field problem.

Q: Decode the following message, which was encrypted using the matrix A. (Include any appropriate…

A: Then given matrix is A =And encrypted matrix is B =

Q: For each real number x, x(1 − x) ≤

A: To prove this by contradiction.Assume that the given proposition is false.This means there exists a…

Q: The cycle type of a permutation is a list of the lengths of its disjoint cycles, from largest to…

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Q: Mark the following either true or false. Justification is required. (a) The dimensions of Col A and…

A: To answer the questions we can use following formula(a) For a matrix A with order m × n, Rank (A) +…

Q: Which pair of the following graphs is isomorphic? O A B and C A and C A and B B с

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Q: b) 2

A: We have to simplify the given expression.

Q: Find T(t), N(t), at, and an at the given time t for the plane curve r(t) r(t) = ti + 2j, t = 3 T(3)…

A: We have to find the unit tangent vector, unit normal vector at t=3 and the Tangential and Normal…

Q: Find the general solution of the system x'(t) = Ax(t) for the given matrix A. 7 -3 4 A = - 13 7

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

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Q: Let A = -2 -3 - 4 4 5 5 1 2 4 1 How can the third column of A be found without computing the other…

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Q: 1) Recall that if X1, X2,...Xn i.i.d random sample from N(u, 2) with unknown μ and o2, then we have,…

A: X1, X2, ....Xn i.i.d random sample

Q: Use the following definition of compactness: KCR is compact if every open covering B of K has a…

A: Let us prove that the union of compact spaces is also compact.

Q: What is the interquartile range (QR) for the data set? 12, 14, 15, 18, 22, 24, 28, 31, 35 0 00 14.5…

A: Given data is Arrange the data in ascending order we get

Q: Given the integral domain ≺D,+,⋅≻ and k,l,m∈D, with m≠0. Then mk=ml⟹k=l.   True False

A: (.)  In an integral domain  product of two non - zero elements is non - zero.i.e.  if  such that

Q: 8. Suppose (an-1 converges to A, and define a new sequence (b)-1 by bn = all n. Prove that (bn)n-1…

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Q: B) Use the given general solution to solve the initial value problems. Is there a unique solution,…

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Q: explain why x=sin^-1(-0.4) is not a solution to the equation sin(x)=-0.4 on the interval (0,2π).

A: We are asked to explain why is not a solution to the equation on the interval .

Q: A Consider the following DAG: L B G D C LL F E Give an example of a topological sort, a maximal…

A: Let us define the definitions one by one......................Topological Sort:The topological sort…

Q: Find U₁A, and A; if for every positive integer i, d) A, (i, co), that is, the set of real numbers x…

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Q: Use Gaussian elimination to find all the solutions (if any) of the following system of equations.…

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Q: Use Lagrange multipliers to find the extreme values of  the functon subject to the given constraint.…

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Q: Solve the inequality to two decimal places where 0 ≤ x ≤ 2π, 4 cos(x) + 2 > π

A: We will use the graphs to solve this inequality.

Q: 1. Z₁ = 1-5i 2. Z₂ = 3 + 2i Z2 3. Z3 = −7+i

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Give a row-echelon form of the matrix A and give its rank: 224-6 0 A = 1 1 2 -2 -4 337 -8 -8 You can…

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Q: Find the Galois group of the splitting field of x + 2 over Q and identify the automorphism and the…

A: Given a splitting field  over .The objective is to find the automorphism and the fixed subfield by…

Q: Suppose the sequence {sn} is bounded above by M and {sn} converges to M. Prove sup{sn : n € N} = M.

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Q: Solve the linear programming problem. Maximize 2=15+15 Subject to 8x+7y 2 128 13x-11 2 29 x+y $ 41…

A: subjected to

Q: solve for y  2xy^2 + 4 = 2(3-x^2y)y', y(-1) = 8

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Q: 7. Consider the following basis B3 of P2(R) and the standard basis E of P₂ (R) B3 = {1+x², x +…

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Q: Answer the following question. Is it valid to apply the gradient and obtain a result of the…

A: Here we have to find the gradient of the given function.

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT DON'T USE AI | DON'T USE AI | DON'T USE AI | DON'T USE AI | 2.…

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Q: Let x, y € Z. Prove that if 2 | (x² - y2) then 4 | (x² - y²)

A: We know that the sum of two odd numbers is an even number.Also, the difference between two odd…

Q: Let T(x) = Ax for the given matrix A. Determine if T is one-to-one and if T is onto. 4 30 6 0 1 3 -4…

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Q: P 356) Let be a given natural number. Give an a sequence (xn) that is not a Cauchy sequence, of пр…

A: We have to find out an example of a sequence which is not Cauchy though it satisfy the condition lim…

Q: 1. Let {an} be a sequence in R with an > 0 and 0 < lim inf→∞ an ≤ lim Supn an < ∞. Prove that 1 lim…

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Q: Let A and B be rings. Define addition and multiplication on the Cartesian product A x B by…

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Q: Urban Community College is planning to offer courses in Finite Math, Applied Calculus, and Computer…

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Q: Part 1 The United States Census Bureau provided the following estimates and predic- tions for the…

A: We have given total world population: Year, tpopulation,…

Q: A fence 25 feet tall runs parallel to a tall building at a distance of 5 ft from the building as…

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Q: A line through (3,5) and (k,12) is perpendicular to a line through (0,7) and (2. 10). Find the value…

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Q: d. cot(x) - csc(x) = sin(x) cos(x)-sin(x) sin²(x)

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Q: Which equation is a quadratic model for the data set? Hint: Use a graphing calculator or a…

A: We have to find the quadratic equation that fit best.

Q: Find the inverse. Select the correct choice below and, if necessary, fill in the answer box to…

A: To find the inverse of the matrix .Concepts used:A matrix  has an inverse if and only if .To find…

Q: When a cold drink is taken from a refrigerator, its temperature is 6°C. After 20 minutes in a 25°C…

A: The temperature of the room is Initially the temperature of the cold drink is After  minutes the…

Q: :. Solve the initial value problem y(x)= dx =√3+ sinx (1+y2), with y(0) = 1. Use t as the variable…

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Q: Find the Laplace transform, F(s) of the function ƒ(t) = t¹, t > 0 F(s) = s> 0

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Q: When using a numerical method to approximate the value of an integral, we expect there to be some…

A: We have given,,where, Error bound in trapezoidal rule:Where M is the maximum value of  on the…