Suppose that the sequence (b converges to 2. Which of the following sequences converges to 4 necessarily? O a (nnb, - 2/7n) O b. (b, + 4 - 2/n) O c. none of the listed sequences O d. (2b,y, + (0.3)") where y, is a convergent sequence

Q: Q1/ is the sequence {a,) converge > sin n

A: We have to find given sequence is convergent or not .

Q: B) Prove that the sequence is convergent, where az = v2, = v2, 2+an, an+1 = %3D n 2

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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: For the following sequence, if the divergence test applies, either state that lim,- , does not exist…

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Q: What is true for the sequence of general terma, =1+(-1)" ? Select one: O converges to 2 O None of…

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Q: The value ofk that makes the following sequence is converge to * : (7/6) as n approach to infinity…

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Q: Q1: Investigate if the following sequence converge or diverge 00 3n2-1 In D0 10n+5n?

A: At n=0, the given sequence tends to infinite

Q: The sequence an is a divergent sequence попе converges to 8 o converges to 0

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Q: Consider the following sequence X, = + +3 for n e N. Let L = lim¬0 Xn. Which of the following…

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Q: Which one of the following sequences converges? OA (-1)". бл + 3 OB. (-1)"- 4n + 6 4n OC In(6n) OD…

A: if limit of an is finite then sequence is convergent

Q: Does the sequence an converge? n(n+1) If so, what does it converge to?

A: We need to verify whether the given sequence converges or not. So,

Q: The sequence (n+(-1)" n Diverges Converges to 0 Converges to 1 Converges to e Converges to 2e

A: Option 3 is correct.

Q: The sequence a, is converges to 0 a divergent sequence попе converges to 8

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Q: The sequence an = n – Vn +1yn+3 converges to the limit

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Q: Which of the following is true for the sequence, Vn? sin(n2) n3 +1 an = Converges to 0. o Converges…

A: Given sequence is  n32sin(n2)n3+1

Q: Suppose that is a convergent sequence and {an} 3n a, = 12· lim 2n+1) Find lim an. O48 OB. 18 OC12…

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Q: The sequence {5}"-1 is: is: 00 O Converges to 10 O Converges to Converges to 5 Diverges. H/5

A: The given sequence is: 5n=1∞

Q: Suppose a,>0 for all n and 2 a, converges , which of the following must converge n = 1

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Q: The sequence a = n is converges to 0 o converges to 8 попe a divergent sequence

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Q: State if the sequence {xn}1 define below is convergent or divergent: fix -1< a < 1, and let xn =…

A: The convergence of the series can be checked by applying the limits to ∞. The convergence of the…

Q: 3. Prove that the sequence sin(n) (0, 1). converges to n n+1

A: We calculate both limit separately as n tends to infinity.

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

A: ∫xn dx=xn+1n+1Divergence:∫a∞1xp dx =converge  if p&gt;1diverge    if p≤1

Q: Suppose that the sequence {an} converges to a, where 0 < a < 1. Prove that the sequence {a}…

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Q: Find the rate of convergence of the following sequence as n → 0o. n +1 lim 1 400 n +2 -1

A: In this question, the concept of rate of Convergence is applied. Rate of Convergence The rate of…

Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…

A: Any real sequence Xn is said to be convergent if Xn converging to a unique real number. That is, if…

Q: The sequence Converges to e Diverges Converges to 0 Converges to 2e Converges to 1

A: First I have written the definition ofconvergent and divergent sequence and then that given sequence…

Q: Let {x„}" and {ym}*=1 be convergent sequences with limits x and y, respectively. Suppose that all…

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Q: We say that a sequence of real numbers (xn)nɛN converges to the real number а, if Ve > 0,3N E N, Vn…

A: Given sequence is xn=-1n+2-n. Definition: A sequence of real numbers xnn∈N converges to the real…

Q: 13. If x1 := 2 and x+1 = 2+1/x, for n 2 1, show that (x,) is a contractive sequence. What is its…

A: Given x1 = 2 xn+1 = 2 + (1/xn) We need to show that (xn) is a contractive sequence and we need to…

Q: Is {-(n2)} n=1 to infinity, a convergent sequence in R with the usual metric?

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Q: Suppose that the sequence (c,) converges to -1. Which of the following sequences converges to 2…

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Q: Q1/ Isthe sequence {a,} converge ? († - ) -

A: If a sequence converges to some limit, then it is convergent; otherwise it is divergent.

Q: Given: Cn . Is the sequence {c, , convergent or divergent? tan-in

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Q: 1. Use the definition of a convergent sequence to show {7 - converges to 7 where {7- is considered…

A: Convergent Sequence in Metric Space: Let be a metric space and let be a sequence in We say that…

Q: Let ƒ : (a, b) → R. Show by example that the convergence of the sequence in part (a) need not imply…

A: Given: f:(a,b)→R f'(xo)

Q: Does the sequence xn ={n=1 converge in (0,1) ? why ? 100 %D

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Q: Suppose the sequence {a,} is convergent, in particular lim,-o an = L. Does this mean that every…

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Q: Suppose xn2 0 for all n E N and the sequence (-1)"xn converges. What is its limit?

A: A sequence represented by say bn; if converges thenlimn→∞bn=0. It is important to note that the…

Q: The sequence (tanh n) converges to2

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Q: By examining the limit as n→0, the sequence {2"}D=1 O Diverges O Converges to 0 1 Converges to

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Q: 2. Use the definition to prove that if (xn) is a sequence of real numbers which converges to -3,…

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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: c) Determine if the sequence b, sin(2an + 5) converges or diverges.

A: To determine whether the sequence converges or diverges.

Q: converges

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Q: Suppose 1 aj = 2 3 4 5 aɔ = az = as = 1 1 3 4 4 5 6. 6. a) Find an explicit formula for a,: b)…

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Q: Find a sequence X, such that it does not converge to any real number, but Y, does converge to some…

A: Consider the sequence Xn=(-1)n. Then Xn={-1,1,-1,1,-1,1,-1,1,...}. So, Xn does not converges to any…

Q: Consider the sequence {x} defined by n n+1 +In(1/n²) ifnis odd Is the sequence divergent or…

A: Since answering more than one question is not in our scope, rest can be reposted.

Q: The sequence a = is a divergent sequence o converges to 8 none O converges to 0

A: Given: an=8nn For sequence, an, if limn→∞an+1an&gt;1, then sequence is divergent.

Q: The sequence an = n- -In+1vn +3 converges to the limit %3D A) -3 B) -1 C) 1 D) +2 E) -2

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Q: Write the first five terms of the sequence: ( +o0 S11 In n n=1 Determine whether the sequence…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.