5. (A Comparison Principle) Assume that a € (0, ∞) and 3 € R. Let {n}n=0; {Yn}n=0₂ and {n}ao be sequences of real numbers such that Xn+1 x0 ≤ yo 20 Show that and Yn+1 Zn+1 αxn + B = ayn+ß, n = 0, 1, .... Zazn + B Xn ≤ Yn ≤ Zn for n ≥ 0.

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Q: 8. Consider a sequence {Cn} of nonempty compact subsets of R such that Cn+1 C Cn for each n > 1.…

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Q: dx 1 The single summation of F(xy n1(el=e lim sint X18 X O a. m+2 C. Ob. k+1 Σ k=1 Σ· k=1 m 3 x m+1…

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Q: 8. Give a closed form for the sum You may assume that Σk=1 k = n(n+1) 2 1x2+2x3+ ... k(k + 1) and…

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Q: (a) Let the interval a, b be divided into n equal sub-intervals such that a = x0 < a1 < x2 < x3…

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A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

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Q: 15. Let z = 2cos0 + i(1 – 2sin0) where -n < 0 < n Show that Iz – il = 2

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Q: 5. Let Z ~ N(0, 1). Find z such that P(-z < Z < z) = 0.85

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Q: 13. (a) Express each of following sum in sigma notation 1 a) 1 + 2 + 113 +... + 1 20 b)…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Suppose r1,r2, . . . is a sequence that contains every rational number. Let 1 1 F = R \U (rk 2k k=1…

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Q: 32. Find the limit of the series: x (1+x) (+x) 1+x2 A) B) xx X+x C) (1+x D) (1+x) E) x

A: Given series is,

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Q: 3.5.4) Show directly from the definition that of (xn) and (yn) Cauchy sequences, then cxntyn) and…

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Q: Let N = (0, 1) and 1 0 such that ||9n||LP (2) ≤ M, VEN

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Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: 7. Prove by induction. For any n2 0, E F = F,Fn+1• k=0

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Q: i) Let {n} a sequence of non-negative terms that is monotone decreasing and în → 0. If SnX1 X2 + x3…

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Q: Theorem 7.10. (Classification Theorem) Let u, v E R with 0 < u < v. Consider the test sequences…

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A: The average value of a function f on an interval a ,b is defined as follows: favea, b=1b-a∫abfx dx

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