Show that x, converges to x.

Q: How to prove {sin(n)} is a bounded seuqence that does not converge?

A: To prove xn=sinn is bounded. By definition, a sequence xn is bounded if it is both bounded above and…

Q: Discuss the Conditions foo which Foudies Segies is convergent?

A: Given: Conditions of Fourier series is convergent.

Q: oblem 3. Use the integral test to determine whether Y converges or diverges.

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Q: 18 For which numbers a does x,+, = a{x,– x) converge to x* = (a – 1)/a?

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Q: Prove that or quari -1+ X.- ズい 2. X. ntl converged number Ja to 2.

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Q: find the value of p which the inegrad converges absauaysconditionally COSY

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Q: If lim bn pe 0= =1 || En=1 a, converges, then En=1 b, diverges.? True False

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Q: Is Uniform convergence of {fn(x)} is sufficient but not necessary to transmit continuity from the…

A: From the theorem stated in step two, we can see that the function is uniformly continuous and we can…

Q: Use the Bolzano-Weierstrass Theorem to show that (Xn) = (1, 3, 5, 7, 1, 3, 5, 7, 1, 3,5, 7, . ....)…

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Q: Use the definition to show that dx 2x2 converges.

A: We have to show that the given integration converges.…

Q: Show by example that Σ(an/bn) may diverge even though Σan and Σbn converge and no bn equals 0.

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Q: Prove that {x_n} converges. Need to use info in a) and b)

A: We have the following information from part(a) and part(b) for any a,b∈ℝ…

Q: State why the following intergral is improper and find the value if it is convergent: 2r (z² – 4) "

A: The given integral is I=∫262xx2-423dx The integral is improper as the integrand is unbounded at x=2.

Q: 6. Let (x,) be properly divergent and let (y,) be such that lim(x,y,) belongs to R. Show that (y,)…

A: To show that (yn) converges to 0, given (xn) is properly divergent and (yn) is such that lim(xnyn)…

Q: If fn is a uniformly equicontinuous sequence of functions on a compact interval and fn → f…

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Q: If o an is convergente then o nan is divergente Select one: O True O False

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Q: Determine whether sec(0)de converges and, if

A: Topic:- application of integration

Q: Test the convergency o f Stan ("

A: According to the given information, it is required to test the convergence.

Q: O Determine whether En=1 st. converges or diverges. Justify your answer by citing a 3n+2

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Q: 1 3 .5 4 X +x

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Q: Show that if each fn is bounded on A and (fn) converges uniformly to f on A, then f is bounded on A.

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Q: 8n Show that fn (x) = x2" – x" is unfiormly converges or not by using uniform norm

A: The given function is  fn(x)=x2n-x8n We show that the function is uniformly converges or not by…

Q: Assume that a is increasing on [a, b]. Note that if

A: Given, α is increasing on a, b. if f∈Rα on a, b, then f2∈Rα on a, b. To prove that if f, g∈Rα on a,…

Q: Use the power representation of             f(x) = 4/(1-x^2) to find its interval of convergence

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Q: If lim,- f(x)=0, then f(x)dx converges Select one: True O False

A: As the mention in above given question when x goes towards infinte than function f(x) gives 0. It…

Q: If lim,f(x) = 0, then f(x)dx converges Select one: O True False

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Q: 2. Prove that (1,1,1,...) converge to 1 in (R,).

A: Convergence of the sequence

Q: It can be shown that lim beb = 0. Use this fact and the integral test to show that k is convergent.

A: Given infinite series is: ∑k=1∞kek Integral test states that the given infinite series will be…

Q: Prove that 「+ X,- ズー 2. 71 ,nyo converged number J2 ヒo

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Q: Find the interval of convergence of the follow X + x² 2 x 3

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Q: Determine whether the statement is true or false. dr is convergent.

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Q: . Use the inegral test to show that =1 converges. 1+n2

A: To solve this question first we check derivative of function is negative for n>0 and then we show…

Q: If (an) tends to infinity and (b,n) is bounded, with bn > 0 for all n, then (an/b,) tends to…

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Q: converge to the same limit.

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Q: Prove that or 「+ X。- ズー 2. 71 number J2 Converged to

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Q: If (am) is increasing and en (an) is bounded by M converges to a, {|a1\, |a|}. max

A: Let (an) is increasing sequence and converges to a,

Q: The integral S x3 converges to Select one: O True False

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Q: If X1, Y1, are two positive unequal numbers and Xn = (xn- 1+ Yn – 1) and y, = Vx, – 1 Ya-1 V n 2 2.…

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Q: If Ea, converges absolutely, prove that Ea,² converges.

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Q: Let                          fn(x) = nx/1 + nx2  (d) Is the convergence uniform on (1,∞)?

A: The given sequence of functions is fnx=nx1+nx2. Compute the limit as follows.…

Q: b) Use the Comparison Theorem with f(x) = - to show whether , g(x)dx is convergent or divergent.

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Q: Show that 2"x" converges if |x| <. n=1

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Q: 4. If (1,) is Cauchy and has a convergent subsequnece (r), then prove that (r,) is convergent and…

A: Given that the sequence xn is a Cauchy sequence and it has a convergent subsequence xnk

Q: Show that Seauence Converse is not tade in gehQlali every Convergent is čauchy But

A: We need to prove that every Convergent sequence is Cauchy but the converse is not true

Q: Use the integral test to determine if -2 converges or diverges. Justify your en n n=1

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Q: If |fn(x)| < an for all x and Ln=1 an converges, prove tha En-1 fn(x) converges uniformly. n=1

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Q: 7. Determine if f In (x") dx is convergent or divergent. Justify your results.

A: Note:- We are entitles to solve the first question, unless specified. To determine:- ∫0eln(x2) dx is…