Mark all of the sequences that are monotonic. {} iS₁=1 {In(n)}1 {cos(n)}1 O {e"}1 ∞ [_n__1² n+1 n=1

Q: Prove that the sequence {sin n + cos n is bounded. =1

A: The given sequence is We have to prove that the sequence is bounded.

Q: Does the following sequence converge? If so, find its limit. If it diverge cos(−2π/3−6/n^6)

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Q: 5. Determine if Σn=3 convergent. cos(NT) is absolutely convergent or conditionally n+1

A: "Absolute convergence" means a series will converge even when you take the absolute value of each…

Q: Consider the following sequence, un+1 = log2 (n +1+ un) for n EN' where u1 = 1. Show that for each n…

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Q: 1. Write out the first eight terms of each of the following sequences: (b) {(-1)"} (a) { // } (c)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub￾parts for…

Q: Given a sequence x₁, x2,... of real numbers, show that cos(x₁) + + cos(xn) exists if and only if…

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Q: n cos(n) V1+4n2 (an) at n→∞o or prove that the limit does not exist: (b) In(1+2n²) - 2 ln(1 + n)

A: 7) a) an=ncos(pi n) /sqrt(1+4n2)b) an)-2ln(1+n)

Q: Consider the sequence of functions {fn(x)} = {n²x(1 – x)"} for x € R and n = 1, 2,3.... (a) Sketch…

A: The given sequence: {fn(x)}={n2x(1-x)n} for x∈ℝ and n=1,2,3,... Choose x=0.5∈ℝ.   a) Sketch on the…

Q: 1. Determine whether the following sequences converge or diverge. If the sequence diverges, state…

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Q: (e) To what limit(s) can the fixed-point iteration In 5 cos(n-1)+2-1+kxn−1−4 1+k converge as n→∞,…

A: Given: xn=5 cos(xn-1)+xn-12+kxn-1-41+k

Q: Find the limit (as n → ∞) of the sequence an = In(2n² + 5) – In(5n² + 2), n > 1. %3D

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Q: 7. The famous Rodrigues formula states that H, (x) = (-1)"e*² (4)" functions for positive integers…

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Q: Find the limit of the sequence an={sin(n)/n}..if it exists.

A: Take limit n tends to infinity for finding the limit.

Q: Write the differential equation and then determine whether you have overdamped,critically damped,or…

A: Introduction: The differential equation of motion of an unforced damped harmonic oscillation is…

Q: Mark all of the sequences that have a convergent subsequence. O{n}₁, where an is the digit in the…

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Q: 3n 14 Determine the rate of convergence of the sequence an sin as n → 0. A. O(1/n^2) B. O(1/n^3) C.…

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Q: Mark each sequence {n} having the property that In In (-1)"n n+1 In |xn = (-1)" In = {cos(nn/3)} 1…

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Q: For the sequence an = n cos n n² +1

A: given a sequence

Q: Mark all of the sequences that are monotonic. {sin(n²)}1 In(n) l n P (2) n=1 { n=1 [n² − 1] n² + 1…

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Q: Consider the following six sequences: Cn = n², dn 6n + 4 7n 3' Wn = n Un - = (-²) * · (27). —2)", Zn…

A: The objective of the question is to analyze the given sequences in terms of monotonicity,…