nst. . Decide whether the fo lowing is convergent In the con ver or ०१en1 ९ase ८a्रlवnee ५e 6+1)4"+ 5^** +(-5)~ in an:= t.

Q: 1 (x + 1)2 dx -2

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Q: Find the Value of p which intagral the Converges, abso leste ly Cosn du- Conditionaly. to Jean de

A: Comment: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Show that x, converges to x.

A: Given that X be a metric space . Let xn be the sequence in a metric space X. Suppose that xn has a…

Q: Which of the following mfinite senes are convergent? Select all that apply. 100 100+50+25+... 1-D0 2…

A: Which of the following infinite series are convergent

Q: Suppose fn:A→ Ris uniformly continuous on A, Vn E N and fn →f converges uniformly on A. Question:…

A:

Q: The sequence {( an+2 )"}1 n=1 O diverges converges to Je3 converges to e None converges to Je?

A: the given sequence converges to

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

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Q: the following saries is absolutely Conditionaly converge check iP Conv. or divergent そ(-1) (a!)?…

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Q: Q: Use the Squeeze theorem to estabich cennergence of the gi , ren Sequence Conr Inx X(X+2)

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Q: Show that if (Sntn) converges to (s,t) in R² with the do ("max") metric, then the sequence converges…

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Q: Determine whether converges absolutely, converges condi- 2" cos n n=0 tionally, or diverges.

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Q: Establish the convergence or divergence of the given sequenoes in full detail: (a) In = n!. (b) %. =…

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Q: Prove the following does not converge uniformly in [0,pi] but does converge uniformly in each closed…

A: We have to prove that the following series does not converge uniformly in 0, π but converges…

Q: (-1)ªn n² + 1 mula converges to a value or diverges withou

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Q: Decide whether the following proposition is true or false. Provide a justification for your answer:…

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Q: Determine If the divergent FoIOLWng intergral is convergent and find its value· or S. i

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Q: Suppose that the sequence of functions {fn} and the function f are integrable on [a, b] and that…

A: Given that,  The functions fn and f are integrable on a,b. fn converges to f on uniformly a,b. an…

Q: Let (fn) be a sequence in L that converges uniformly on 2 to f. If µ(2) < ∞ show that…

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Q: Determine whether each of the fo for convergence/divergence. (a) n +1

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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

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Q: the valu e of P. for ubich for allna). fntegral Converges

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

A: Topic:- application of integration

Q: f fn → ƒ uniformly and the functions fn have only jump discon- sinuities, prove that f has only jump…

A: Here we use epsilon delta proof

Q: of the given improper in tegrals convergent. are sinz da 1. ース? de

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Q: Determine i it convergcs or dverges. Evaloate if converges oo dv 2.

A: We have given,

Q: . Use the inegral test to show that =1 1+n2 100 converges. hDoes the alternating serios tost anply…

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Corver Is absdutely contergent, Conditionally Convergent, on divergent

A: Use Alternating series test, P- series test

Q: Exomples Porfrm 2 Thera trons of a a convergent fixed pornt methad to approximate the root of the…

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Q: #2. Give a counter exa mple that (Sn) is bounded but not convergent.

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Q: 4. Suppose fn:A→ Ris uniformly continuous on A , Vn e N and fn →f converges uniformly on A.…

A: Given: fn: A→ℝ is uniformly continuous on A ∀n∈ℕ To prove: fn→f converges uniformly on A  fn→f…

Q: dx Determine if the improper interal S, xc Fnd it valne if it converges. Conneeges on diree jes.…

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Q: Prove ca) lim (an t anay t --- + that if Ean Converges, then + antr) = 0, (b) Give o7Convergence…

A: We have to use properties of convergent series first.

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

A: Convergence of the sequence

Q: converges, then C„-)" " con COr n=0

A: We have to choose the correct answer from the given option according to the given series

Q: of Eca 4 is cenvengend can we conclude that cach of these are convergent: (b) E cn (-4)^ ca)

A: Given that ∑n=0∞Cn4n is convergent.

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

A:

Q: A) diverges B) converges

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: Find all real numbers p for which the improper integral ∫∞1t−pdt∫1∞t−pdt converges. For what values…

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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: Show by example that E(a,/b,) may converge to something other than A /B even when A = equals 0. Σαν…

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Q: What does the nth-Term Test for Divergence say about the following scrics? use the Integral Test to…

A: if integral is finite then series is convergent

Q: ** Consider the sequence (xn) in R, where n (-1)". Show that (rn) doesn't %3D converge to any limit.

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Q: Show that if (sn,tn) converges to (s,t) in ℝ2 with the usual d2 metric, then the sequence converges…

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Q: 3D (2Vn +1)n

A: The given series is,∑n=1∞2n2+1n

Q: The set S on wc fn Cx) = 1+ x" Converges pointwire ?

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Q: Determine if the following is convergent or divergent: I dr

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Q: Perform a testto determine if. S a J y converges diverges or

A: