Show that any sequence of positive real numbers either has a subsequence that converges, or else a subsequence that diverges to ∞. With proof.

Q: Simplify. (²) ² [(15+)-9]

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Q: (a) The sum of infinite number of terms in G.P. is 20 and the sum of their squares is 100. Then find…

A: (a) THE SUM OF INFINITE TERMS OF AN G.P a,ar,ar2,ar3,............arn-1,arn,...... IS GIVEN BY ,…

Q: Find all the eigenvalues and the corresponding eigenvectors of the matrix A = = 6 2 -2 2-2 5 O 7

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Q: Suppose that r(u)r(u) is a vector valued function of uu, and suppose…

A: As per the question we are given a Parametrized curve r(u) in 3d and its derivative at u = 3 as:…

Q: When solving the y" - Ay=0, 0<x< 1, Sturm-Liouville boundary value problem subject to the y' (0) =…

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Q: 2. Let f [a, b] → R be bounded. Prove the following a. If k ≥ 0 then U(kf, P) = kU(f, P) and L(kf,…

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Q: Discrete mathematics Proof by contradiction. Assume for the sake of argument that the set P of all…

A: Here we want to prove that the set of prime numbers is infinite. Proof by contradiction is given. We…

Q: frequency 8 4 2 1 2 3 4 5 6 Do the data appear to be normally distributed? Explain. O Yes, the…

A: The dice is rolled: So, the outcomes can be 1, 2, 3, 4, 5, 6 So, Die Rolled frequency 1 7 2 5…

Q: The first four Hermite polynomials are 1, 2t, -2 +41², and 12t+8t³. These polynomials arise…

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Q: Consider the following initial value problem, in which an input of large amplitude and short…

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Q: H be the set of all points (x, y) in ℝ2 such that x2 + xy 3y2 = 3. Show that H is a closed subset of…

A: Answer given below.

Q: Please answer this correclty and I will give a thumbs up, thank you!

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Q: 21.5 Integrate the following function both analytically and using Simpson's rules, with n = 4 and 5.…

A: Given: ∫-354x-33dx We have to evaluate the integral analytically as well as by using Simpson's rule…

Q: م کا ہے اور بر م permetry fregresse ce the furm it them find the llowing ratio of the que do

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Q: Show that the solution of the equation [ X Z [± √aß - a 1- -ß √aß X [ *] =0 is where a, ß are…

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Q: Ife is defined as e¹=I+A+ where A = *].0<** the functions f(x) and g(x). 4 + 4 + 4 + -1 [1(x) 8(x)]…

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Q: Find a general Solution to the given equation for to E²Y" (t)-ty' (t) + 47 (E) = 0 7 The general…

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Q: Given: BD AC, BAI AD and ADL DC. Prove: ABAD ACDA. Step H 2 try Statement BD AC BAAD AD 1 DC AD AD…

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Q: 1. During the dry season, a state extensively cultivates maize crops. The average weight (in kg) of…

A: Given Data: It is given that the average weight is hx,y,z=240+y2ln2x-z-75z, where,x is the average…

Q: dependent: --8--8---8---8 V3 = VI 1 0 V2 = 2 V4= 3 4 Solve c₁v₁ + c₂2+ C3V3+ C4V4 = 0 or Ax = 0. The…

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Q: A raffle is going to be held in which the winner will get $200. If 1000 tickets are to be sold, what…

A: Given, In a raffle, winner will get $200.    We have to find the fair price for a ticket if 1000…

Q: If a, b, c, d and p are distinct real numbers such tha (a² + b² + c²)p² - 2(ab + bc + cd)p+ (b² + c²…

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Q: If w In(4xy) 22 du - cos(2yz -3), z log(t), y - 4e and z-sin(-1). Find 5 - dt

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Q: Given the vectors (1 10), (0 2 3), (1 2 3) in R3. Given vectors are linearly independent. Select…

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Q: respectively

A: Part a

Q: Determine whether each of the following series are absolutely convergent, conditionally convergent,…

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Q: 3.a solve please

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Q: (c) Find a power series representation for fx arctan(x) dx. You can use the sigma notation or the…

A: Here we use series for arctan x. Also in the last question we use Taylor error approximation.

Q: 1. 2(2,3)-3(-1,2)+2(1,1) is a linear combination for what vector? a. (9,1) b. (9,-2) c. (9,0) d.…

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Q: Transform the given system of differential equations into an equivalent system of first-order…

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Q: Is the following argument valid? PV q r →=p q r

A: Use the truth table method to check the validity of the argument.

Q: Subject Name: Linear Algebra Tips: please solve problem-1 and must do it handwriting on a paper

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Q: Find two linearly independent vectors perpendicular to the vector v = نا دیا دیا -3

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Q: Can you use the method of partial fractions

A: We have  ∫180-x60-xdx=k∫dt We have to solve using partial fraction. Let 180-x60-x=A80-x+B60-x

Q: Show that 1 3+2 4+3.5++ n(n+2) = 1.3= 1(1+1)[2(1)+7] 6 Simplify S₁ on the right. 3= 3 Is S₁ a true…

A: Given that the statement is Sn: 1.3 + 2.4 + 3.5 + … + n. (n + 2) = [n(n + 1)(2n + 7)]/6 Now let us…

Q: metic progression whose common difference is nonzero, the sum. qual to the sum of next n terms.…

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Q: 5.6.34. (a) Find an example of set A and a nonempty subset B C A, such that A and A \ B have the…

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Q: Find the positive real root of  ax3 - bx - c = 0 if a = 0.4, b = 5, and c = 9 using bisection method…

A: ax3-bx-c=0 a=0.4b=5c=9

Q: Question 3 Consider the differential equation x²y" - 3xy' + 3y = 2x³ - 3x². (a) Verify that y₁ = x…

A: x2y''-3xy'+3y=2x3-3x2

Q: . Use separation of variables to find the product solution for the given differential equation. 82u…

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Q: 2. a. Find the value of 21-dx x b. Use the trapezoidal rule with four trapezoids to find an…

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Q: Match the following 10 functions into 5 pairs. If f(n) is paired with g(n) then f(n) = 0(g(n)), log₂…

A: As per the question we are given 10 different functions from which we have to find the 5 pairs in…

Q: Define a binary relation =3 on Z by x =3 y if x - y is divisible by 3. 1. Prove that = 3 is an…

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Q: Write the corresponding statement of each proposition if p stands for "Thermodynamics is a branch of…

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

Q: Based on the data shown below, calculate the regression line (each value to two decimal places) y…

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Q: Let R = ({0, 1,,8), 0, 0) be a ring where and are defined as follows: a b = (a + b) mod 9 a Ob= (ab)…

A: Using the definition of the Ring R we answer all the questions. Important thing to note is the using…

Q: 4. Solve the linear equation systems 2x, +5x₂+2x, = -8 by using Crout method, where (x₁+2x₂ + 3x₂ =…

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Q: Given the following set of the vectors from M22 We can not express Select one: O True O False Give…

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Q: 2. Determine y when x = 2 using the fourth order Runge-Kutta algorithm, in five decimal places, for…

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Q: Question 2 [ Let f(x, y) = 6-3y³-yr² +22² +2y² and h(x, y) = 2x² + y². Find all the local maximum…

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