1. Consider the following sequence xn = 여 1 1 4m, if n is odd 4n-2, if n is even Compute lim sup and the lim inf of xn, as n→∞. Show work.

Q: Let x₁ = 5 and x n+1 = X n 2+4 2x n n 1. Find lim x " n n→ ∞

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Q: Evaluate the limit. 1² – 4x + 3 lim 3x3 21 +3

A: To evaluate the limit limx→∞x2-4x+33x3-2x+3

Q: Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using…

A: Given: (sn) and (tn) are sequences so that sn = tn except for finitely many values of n and…

Q: Find the limit

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Q: Let An= [n, n+1] and Bn= Lo,3++ for all neN 9 (UAn)= lim ML (An) %3D n-> DO %3D HL ") ML (U Bn ) = 3…

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Q: EX.3: Use the M-N definition to show that lim (n - 10n2 – 6n + 3) = 0.

A: According to M-N definition, Let, an=n3-10n2-6n+3                                 ...1if…

Q: 1 lim E n→ 00 i=1 'n² + i?

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Q: 10. Find each limit if x→∞0 a) lim 3-2x 3x x² + 3x-18 (x-9)² b)lim- 7 x +31 c) lim(5x +4--

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Q: 2. SOLVING HLDECC USING AUXILIARY EQUATION ²+k²x = 0, k is real number; when t = 0, x = 0,= vo. dt…

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Q: Which of the following subsets of R satisfies the following property: If (x,) is a Cauchy sequence…

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Q: Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using…

A: Given : sn , tn are sequences such that sn=tn except for finitely many values of n and Limn→∞sn=s.We…

Q: 11. (a) Evaluate: lim 5x

A: a) We have    limx→05x-83=5limx→0x-83                   =50-83                   =5083…

Q: Compute lim 400 2017 2017 / k+1+k+专 十 + 2017** 十店

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Q: lim x → 0

A: →When limit is of the form 00 or ∞∞ then we use L'Hospitals Rule  →In L'Hospitals Rule , take…

Q: 3 show that if lin N-)P number . an = a, then lim 29 = 2a for all real 3-)

A: Given : limn→∞ an=a To prove : limn→∞  λan=λa.

Q: If a sub 1=1 and a sub (n+1)=3 - 1/a sub n, what is the limit of a sub n as n approaches infinity

A: Limit

Q: 2. Prove that a. lim, b. lim,1

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Q: Let limf(x)=L(Lbeanyrealnumber) andnbe apositive integer. X→C Whichof the givenstatementsis/are…

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Q: 2 2 - Let S₁ = 3x₁² x₁ + 3x₂² Ax₂ +...+ 3x² Ax, where the Ax;, fill out the x-interval from x = -2…

A: Given that Sn=3x12∆x1+3x22∆x2+...+3xn2∆xn, where the ∆xi fill out the x-interval from x=-2 to x=6…

Q: how can i apprach this problem

A: The objective of this question is to find the limit of the sequence (n+1) as n approaches 0 using…

Q: 23. lim 1 /n² +1

A: To prove: limn→∞nn2+1=1

Q: Find the limits

A: To evaluate the limit: lim1x2-4 (a). When x→2+. Evaluating the limit. limx→2+1x2-4=12+2-4=10+=∞…

Q: Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using…

A: Given that sn and tn are sequences so that sn=tn except for finitely many values of n. If…

Q: 74 t4 - 1 lim t→l t³ – 1

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Q: . Find two sequences {an}o and {b»}_o such that lim 0o. As part of your solution, explain…

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Q: (14) Suppose that (x„) and (y„) are sequences. Prove the following. (*) (c) Let k > 0. If lim (x„) =…

A: The sequence xn and yn. Then,

Q: 10. Prove that if lim(x,) = x and if x > 0, then there exists a natural number M such that x, > 0…

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Q: Let an 2n+4n-3 Using the definition of the limit, prove that lim,∞ an 3n2+2n+1* 2/3.

A: Given that, the rational function  an = 2n2+4n-33n2+2n+1 To prove that limit of function is limn→∞…

Q: lim x* + 5x2 – 12x + 3 x→-2

A: Given function is: limx→-2x4+5x2-12x+3

Q: -1 Suppose that (an), has an >0 for all n. Show that lim sup a, = (liminfa,)¯. Suppose (an)=1 and…

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Q: 8. True or False: If lim an = 0, then an converges. %3D n=0 (a) True (b) False

A: Solved below

Q: 7) Show that lim = 1. 200 (z-i)3

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Q: Compute lim 0 tan-(5x) 5 25 undefined 1 25

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