If X1, Y1, are two positive unequal numbers and Xn = (xn– 1+ Yn – 1) and y,= Vx – 1 Yn –1 V n 2 2. Prove that the sequences ( x, ) and (y, ) are monotonic and they converge to the same linit.

Q: Q2 Prove that the scries 2+ x2 3+X2 4+x is Unitormly convergem? in any interval?

A: The given series is: 11+x2+12+x2+13+x2+……. Therefore the given series can be written as:…

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A: Given that sequence pkk=1∞ converges to point x.

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Q: Let {fn(x)} : „x ER and > 0. 1+ nx Show that ift>0, the sequence {fn(x)} converges uniformly on

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A: Consider the sequence  fnx=n2x1-nx      ,x∈0,1n0                       ,elsewhere The limit function…

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Q: . Find all values of x for which пх" n=1 (n + 1)(2x + 1)" converges absolutely.

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Q: (a) Prove that (2x + 2) > 1 for all x > 0. (b) Let so > 0, and sn+1= } (2s, + ) for all n > 0. Prove…

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Q: If 2 a, converges, then la,| diverges. n=1 n=1 True False

A: Given statement is FALSE. I HAVE given a counter -example.

Q: Suppose xo = 2√3, yo = 3, 2xn-14-1 Xn-1+Yn-1 and Prove that (a) xnx and yn ↑y as n→ co for some x, y…

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Q: Show that the sequence of functions {f.} where f,(x)=: 1+ nx „xER is non-uniformly convergent on…

A: Show that the sequence of functions fn(x), where  fnx=x1+nx2,  x∈ℝ is non-uniformly convergent on…

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

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Q: 1.1 Determine whether the sequence (Jn(x)} = {, on I = [0,1]. %3D I7 converges uniformly

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: Suppose that F(u) denotes the DFT of the sequence of f(x)={1, 2, 3, 4}? What is the value of F(14)?…

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Q: 3 If Xn 4 and ly,l0. Select one: True O False

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Q: 2. Prove that (1,1,1,...) converge to 1 in (R,).

A: Convergence of the sequence

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Q: Consider the sequence S n²r(1 – nx) x € [0, 1/n] - fn(x) := 0. elsewhere . Show it converges…

A: Let gx=n2x1-nx Differentiating wrt x, we get  g'x=n2-2n3x Putting g'x=0, we get  n2-2n3x=0⇒x=12n

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Q: Suppose {fn}n=1 and {gn}n=1 converges uniformly on E where {fn}n=1 and {gn}n=1 are sequences of…

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Q: 4. Let (#1, y1) = (0,0) and let (n+1, Yn+1} = (2+ yn, 3 – Tn) for n > 1. Prove that (Cn, Yn) is a…

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Q: Suppose And Xxn Xo = 2√3, Yo = 3, Yn 2xn-1Yn-1 Xn-1 + Yn-1 = √XnYn-1 For all n E N Prove that Xn…

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Q: Let (X,) be a sequence of real numbers. If for some x e R, (X,) converges to poth 7x + 2 and 2x - 13…

A: which of the following statement is true.

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Q: 5. Show that the sequence Pn = 1 converges linearly to p 0, and the sequence Pn = 10-2" converges…

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Q: Suppose that fn(x) and f(x) are functions R –→ R. Suppose also that fn converges uniformly to f as n…

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.