pute the following limits of sequences. 1 n2 + 4" + 3e" 4n3 + 5n + n! + 7 lim n→0

Q: 3+n bn

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Q: By squeeze theorem, the sequence an= is n2 converges to, OA. 0 OB.1 Ов. Oc. D.

A: The given sequence lies between limn→∞cos-πn2 and limn→∞cosπn2.

Q: One of the following sequences is divergent ( 2n en n=1 n? {(-1)" n² + 1 J n=1 {-1", 3n ) (-1)n. n2…

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Q: Which of the following sequences is strictly decreasing O None 1 n+ 3 S n=1 In+3 n=1

A: Given: 1n+3n=1∞

Q: One of the following sequences is divergent S 2n ] en n=1 3n (-1)" . n2 +7 ) n=2 None {8}=1 n2 -1)"…

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Q: Q22. A Sequence has been defined as the following Tan aj = 1, ɑn+1 2 + an You must find its limit,…

A: a1=1,  an+1=7an2+an

Q: For each of the following, make a claim about the convergence of the sequence and use the e-N…

A: To find - For each of the following, make a claim about the convergence of the sequence, and use the…

Q: 6. For each of the following sequences, find the limit and show your reasoning. (-1)" n! n2 + In n…

A: To Find: i. limn→∞-1nn!2nn,ii. limn→∞n2+lnnn+en

Q: 2n b) ɑn n²+1

A: b) To find the first five terms of the given sequence is: an=2nn2+1

Q: Determine the limit of the sequence a, u UIS 3 Ve Divergent 4 1 5

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Q: Determine the limit of the following sequence and prove your claims a. an=n/n2+1 b. bn = 7n-19/3n+

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Q: Find the limit superior and limit inferior of following sequences sin() • an = n n = 1, 2, 3, .. if…

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Q: I. Determine whether the following sequences are convergent or divergent. Then justify your answers.…

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Q: One of the following sequences is divergent S 2n l Ten In=1 3n ° 1)" n² +7. n=2 O None n- -1)" n² +…

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Q: Find the limit of the following sequences or determine that the sequence diverges.

A: Given sequence {bn}, where     bn=nn+1      if n≤5000ne-n       if n>5000   If the limit exists…

Q: Determine the limit superior and limit inferior of the following sequences: {1 1 1 (a) = 4 5

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Q: Which of the following sequences is strictly decreasing 00 In+2 n=1 n+2 J n=1 n + 1 O None

A: Decreasing sequence.

Q: 1. Compute the following limits of sequences. (n2")² (a) lim n+00 no + n² In(n) + n²3" ° 금급 +4" +…

A: If the fraction after putting the limits results in ∞∞ form then changes have to be made to change…

Q: Evaluate the limit of the sequence or state that it does not exist. an = (-1)n (3n3 + 4n)/(6n3 + 5)

A: Given sequence: an=(-1)n(3n3+4n)(6n3+5) To find the limit of this given sequence:…

Q: Which of the following sequences is strictly decreasing 1 n+ 1 n=1 O None {(-1)"}} n-1 {n꾸I} In+1…

A: Strictly decreasing sequence

Q: 2. Use the derivative test to determine if the following sequences are monotonic increasing,…

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Q: Use the limit comparison test to find the sum from k=1 to infinity of: [(5sin2k)/k!]

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Q: Which of the following sequences is convergent? Select one: O a. lim, v00 n² +1 3n /n15 n2 cos(1/n)…

A: b

Q: Find the limit of the sequence {an} if 1 - (1)/(n) < an < 1 + (1)/(n), forevery integer n ≥ 1.

A: Given: 1-1n<an<1+1n where n≥1 We have to find the limit of the sequence an:

Q: 6 If (rn) and (yn) are bounded real sequences, show that sup(n+yn) ≤ lim supan + lim sup yn lim 84x…

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Q: Let (xn) be a bounded sequence and let s = sup{xn : n e N}. Show that if s ¢ {xn : n E N}, then…

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Q: 2 {a,} =- Vn? +7n - Vn² +2n.

A: We have to find the limit of given sequence.

Q: Which of the following sequences is strictly decreasing 8. n+ 1 n+1 S None

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Q: Compute the limit of the sequence given recursively as follows. If the limit does not exist, enter…

A: To determine the value of the limit.

Q: 43. Let {rn}-1 be a bounded sequence and {y„}=1 be a sequence tending to 0. Pro that x„yn → 0.

A: We have given that , xn be a bounded sequence. Also , yn be sequence tending to 0. We need to prove…

Q: Suppare Hhat Inf is a fonvergent sequence famarging that the set {:X=Xn for Summe n has prackly one…

A: Let xn be a sequence of numbers converging to L. To prove that L is the only accumulation point of…

Q: 103n2 – 8 - 1. Xn := 4n2 + 99n + 3 1i. Xn := -n + Vn² + 3n 3n? + 2n iii. Xn := 2n n=1 8.

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Q: use the appropriate limit laws and theorems to determine the limit of the sequence orshow that it…

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Q: Which of the following sequences is strictly decreasing n+ 2 S =1 n+ 2 00 {-1)" 1n+ -1

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Q: Find the limit of the following sequences or show why they diverge. n2 – 2n + 1 (a) - en n+ (b)

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Q: Evaluate the limit of the sequence or state that it does not exist. an = (n2 + 4)/√(4n4 + 1)

A: We have to find the limit of the sequence: an=n2+44n4+1 So finding limit, limn→∞n2+44n4+1 As it is…

Q: 00 00 Show that > n3 + 8n converges by using the Direct Comparison Test with En3. n=1 n=1

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Q: Which of the following sequences is strictly decreasing None 1 {-1)",! n+ 2 S n=1 n+ 3 n=1 00 1 n+3…

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Q: Find the first 5 terms of the following sequences a k for k >0 2k +1 a) Let ak

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3"2"+3 {d,} =- 4" n! in.

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Q: Which of the following sequences are bounded? Select all such sequences. X That's not right. 6n…

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Q: Find the limit of the sequence πρὖ + 4 πρ4 +5 c3 - 2e { where - e CER+ and n " cn+1 - ne 0 for any…

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Q: Give the limit of the following sequences. nV14 - 3n? +* 7n + 2n An 3n – 4 2nn B = sin 3 n* + 2nv2…

A: As per our guidelines, we are supposed to solve only first three subparts. Kindly repost other…

Q: Which of the following sequences is strictly decreasing n+2 {(-1)"} n+1S -1 O None n+2

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Q: Which of the following sequences is strictly decreasing {(-1)"n+2 S n=1 00 n+ 3 n=1 O None n + 3 S…

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Q: Of the following sequences, which are bounded? Select all such sequences. Select all that apply: O…

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Q: Which of the following sequences is strictly decreasing {-1)" } }", 8. O None n+ 1 S_n In+1 S 1

A: Write some terms of sequence And find limit of sequence

Q: Which of the following sequences in R is convergent? (a) x_n= n + (3/n) - (b) x_n= −1 + ( [(-1)^n]/n…

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts.…

Q: One of the following sequences is divergent 3n (-1)n n2 + 7 n=2 3. n=1 (-1)* n=1 O None

A: