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: Find the limit

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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: 11. (a) Evaluate: lim 5x

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

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: 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: 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: 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: lim x* + 5x2 – 12x + 3 x→-2

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

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

A: Solved below

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

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