. Let x₁>1 and Xn+1 = 2 - 1/xn for n E N. show that (xn) is bounded and monotone. Find the limit

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Q: Prove the following Lemma 3: if x > 0 then 1/x > 0.

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A: according to guidelines we can do only first question thank youLet a and b be integers with GCD(a,…

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Q: Prove the following Lemma 2: if x, y ER and x 0.

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Q: Refer to the graph of y = f(x) to the right to describe the behavior of lim f(x). Use -∞o and ∞o…

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Q: At: xy'=y+(x^2 +y^2)^1/2   you multiply by 1/x to get the y' = dy/dx... But wouldn't the right side…

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Q: 2a. Write a MATLAB command that creates a row vector u that has the elements: Cos 3e 19π -2e, log10…

A: 2a. We write MATLAB command that creates a row vector u. Then we will find the maximum value of…

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A: A system of equation Ax=b has infinite number of solution if and only if the rank of the augmented…

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A: Given that from the problem :F1  =35.0 lbF2 =135 lbMA =175 lb-ft

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Q: a contractor must tile a rectangular kitchen that is 8ft longer than it is wide and the perimeter of…

A: A contractor must tile a rectangular kitchen that is 8ft longer than it is wide and the perimeter of…

Q: (1 pt) Express the following limits as integrals. (a) L₁ : = n→+∞ where a = n lim Σ k=1 L₁ = (b) L₂…

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Q: Lemma 1: if x, y ≤R and x > 0 and y 0. Lemma 3: if x > 0 then 1/x > 0. Lemma 4: if x 0 and b 0.

A: Here both a and b are real numbers. So, both a and b are either positive or negative.We will…

Q: 3 Write MATLAB commands that do the following: Create the following matrix by using shorthand…

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Q: OLVE STEP BY STEP IN DIGITAL ORMAT Lim 818 (1 + 2/2 ) *

A: The given limit is Lets use the method of Taylor's expansion.

Q: Find y as a function of t if y(3) = 2, y = y'(3) = 2. 25y" +90y + 162y = 0,

A: We find y as a function of t 25y'' +90y'+162y=0,y(3)= 2, y'(3)=2

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Q: Consider the following. u = (5,7), v = (6, 2) (a) Find the projection of u onto v. 33 11 5' 5 (b)…

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Q: The water in a river moves south at 3 miles per hour. A boat travels due west at a speed of 25 miles…

A: The water in a river moves south at 3 miles per hour. A boat travels due west at a speed of 25 miles…

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A: The problem is to check the origin is in the line passing through the point  We know that the…

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Q: Solve the following LP Maximize $4x + $5y Subject to            2x + 3y ≤ 20 (labor, in hours)…

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Q: What is the value of ¡4n+1 ¡4n-1

A: The given expression is here

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Q: The two curves below describe the numbers of people in two countries at time t, in years. Answer…

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Q: E. i. Prove directly from the definitions that if g: R → [1, ∞0) is a function so that limx→ g(x) =…

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Q: For the given scenario, identify the type of growth as linear, exponential, or neither. Ephraim owns…

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Q: 3.2.1 Vector Cross Product Let vectors: A = (1, 0, −3), B = (–2, 5, 1), and C = (3, 1, 1). Part…

A: Since, you have posted a question with sub-parts greater than three. We will provide the solution…

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A: A local car rental company recorded the cost of the rental versus distance travelled by the customer…

Q: Question 6 Determine the area of the region in the first quadrant enclosed by the graphs of x = y²…

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Q: Consider the following dataset:     9   11   25   44   60   79   97  Find the percentile rank of…

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Q: Determine whether the statement below is true or false. Justify the answer. The set Span (u, v) is…

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Q: Solve the differential equation, subject to the given initial condition. dy Xdx +4y=5x? y-0 y(2) =…

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Q: 2. In how many ways can the letters of the word GRADIENT be arranged so that two vowels are not…

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Q: This year Tonya's average golf score was 103 strokes for 18 holes. Her goal over the next 10 years…

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Q: If ƒ(x) = 1/(1 + x) show that Tn (ƒ,0, x) = Σk_o(−1)kxk.

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Q: wrong. 3. What is the angle of elevation for the pyramid in Question 2, to one decimal place? Mark…

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Q: t) Find the area under y = -x² + 1x + 12 and above the x-axis using Riemann sums. ·b S² (-2²² + a…

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Q: C. Show that both R and R² may be covered by countably many open balls.

A: Firstly we have shown that R may be covered by countably many open balls. Let us  consider the set…

Q: Show that y=cx-2 is a general solution of xy' = y +2, where c is an arbitrary constant and find c if…

A: We have to show that y= cx-2 is a general solution of xy' = y+ 2. If y(1)=3, then we have to find c.…