6. Consider the folowing sequence of functions. n fn(x) = , х€ (0, 1) nx + x a) Find the pointwise limit function. b) Is the limit function bounded?

Q: Q4: Consider the sequence (f, (x)) of functions f,:R→R defined by : nx f,(x) = Ji+n°x² Find the…

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Q: Give an example of a sequence an whose set of subsequential limits S = {a €RU{-0}U{x} : a = lim ak,…

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Q: Let {an}=1 be a convergent sequence such that a1 = V5 and an+1 = V5 a,n. Compute lim an.

A: The sequence an is convergenta1=5 and an+1=5 an

Q: 3. Suppose {fa) is an equicontinuous sequence of functions on a compact set K, and U.) converges…

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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: 1. Let {an}1 be a convergent sequence such that V5 and an+1 V5 a,. aj = Compute lim an.

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Q: Let {xn} be a bounded sequence on R. Show that lim = 0. n→+∞ n

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Q: 9. Find the limit (if it exists) of the sequence (x_n) where x_n= n-3n^2.

A: Given xn=n-3n2

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Q: Prove that the sequence given by 2.4. 6.(2n) Un = 3.5.7.…(2n + 1) converges and find its limit.

A: Given query is to prove that sequence converges.

Q: 4n +1 tan 2n %3D What is the limit of sequences n

A: Given sequencean=4n2+1ntanπ2n

Q: + R be defined by fn(x) = an Find the pointwise limit in 1.3 converges uniformly on [–3, 3]?…

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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: Let {xn} be a bounded sequence on R. Show that Xn lim = 0. - n→+o n

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Q: n2 – 1 - at the sequence ɑn is eventually stric n2 + 2 so show that {a,} is bounded above. What can…

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Q: 1. Prove the sequence (a,} = (1+" Converges to the limit e*, what about the sequence {b,} = (1-5?…

A: Note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Let {xn} be a bounded sequence on R. Show that Xn lim = 0. - n→+∞ n

A: follow next step

Q: Compute the first six terms of the sequence {an} = {n√n}. If the sequence converges, find its limit.

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Q: Find the limit of the sequence {an} = {-Yón}. Enter as an exact value. V 4n+1 limn→o An help…

A: To find the limit of a given sequence.  {an}.

Q: Q. Find the limit of next sequence using the theorem for Limits n +1 2n'+1

A: Consider the provided question, given,  n2+12n2+1 We need to find the limit of the above expression,

Q: Assume (fn) and (gn) are uniformly convergent sequences of functions. (b) Give an example to show…

A: Given : Assume (fn) and (gn) are uniformly convergent sequence of functions.

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Q: Find the limit if the sequence converges and lim sup and lim inf if the sequences diverges (c and d)

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Q: 3Vn + 13 Determine whether the sequence an converges or diverges. If it converges, find the limit.…

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

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Q: Let a and b be constants with 0 < a < b. Does the sequence {(an + bn)}^1/n converge? If it…

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Q: 15. Let s1 = 3 and Sn+1 = 6+ Sn for n >1. Show that the sequence {Sn} %3D %3D is bounded and…

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Q: 4. Consider the folowing sequence of functions. 5+ nx? fn(x) = , x E [0, 1] 5+ nx a) Find the…

A: (4.) We will find the all step of the function.

Q: Q\ Find the limit points of all subsequences of the sequence ((-1)²" – (-1)*"),nen

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Q: A material transmutes 50% of its mass to another element every 10 years due to radioactive decay.…

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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: • Let (xn) and (Yn) be bounded sequences and xn < Yn. Show that lim inf xn < lim inf Yn . n00

A: Sequence question

Q: The sequence {an} is defined by a1 = : 2, and An + An An+1 = for n > 1. Assuming that {an}…

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Q: Let x1 = 1 and define xk+1 = sqrt(2xk) where k is a natural number. Prove that the sequence {xk} for…

A: Given: x1=1, xk+1=2xk So, x2=2x1=2&gt;x1 x3=2x2=22&gt;x2 On generalizing, we get…

Q: 28. yn = ne/n

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Q: п+1 2n +1 dn + Vn² · 6n+1. 2n ||

A: Note some standard results of limit: limn→∞ 1+1nn=e limn→∞ n1n=1 Suppose xn and yn are two…

Q: 5. Show that the infinite sequence a, = Vn2 + 1 – yn² – 1 (n 1) converges by showing that it is…

A: Given sequence is  an= √(n^2+1) - √(n^2-1)

Q: 6. ) Let. f: R R be continuous and let {an} be a bounded sequence in R such

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Q: 2 TE an=n2(cos(+ %3D Find the limit of the sequence (a„), if it is convergent. Otherwise, please…

A: Explanation of the answer is as follows

Q: Use the definition of the limit of a sequence to prove that 3n +1 lim 2n + 5 3 %3D 21

A: We need to use the definition of the limit of a sequence. we have the definition of limit as,…

Q: 1. Show the sequence an (n+1)/(n-1) is strictly decreasing and bounded %3D below, and give its…

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Q: -Let a = 1 and define an+1 = /4a, – I for n 2 1. Show that the sequence {an} converges and find the…

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Q: 1 dx where p> 1 %3D xP

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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: Let {xn} be a bounded sequence on R. Show that Xn lim = 0. n→+∞ N

A: Given sequence {xn} is bounded we want to show that  limn→+∞xnn=0 we  use the limit limn→∞1n=0

Q: Find the limit of the sequence using L'Hôpital's Rule. 1(Vn² + 11 – Cn = n - n (Use symbolic…

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Q: converges, what is its limit? 2) ) (In(1+ 4n)) In(n + n=1

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Q: A) If (xn) is a decreasing and bounded sequence. Prove that (x,n) is convergent with lim xn inf {xn…

A: Multipart :    xn  is decreasing and bounded sequence. To show that , xn is convergent and limn→∞ xn…

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.