04: A) Discuss the convergence of f,(x)=x+- -.on A [0,0).

Q: tan (x) +n In(n+2) 04: Determine the convergence of , on A=[0,+).

A: given fn=∑n=1∞tan-1xx2+n2lnx+2  on A=[0,∞) claim- to determine the convergence

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: Determine the convergence or divergence of serie sin Σ 6n2 n +4 n=1

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Q: Cn an+a2n

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Q: Find the radius of convergence for En-o(-1)" (2n + 1)z".

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Q: Consider fr2/3 dr. Compute the experimental order of convergence when us- ing (a) the composite…

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Q: 3. Define fn on (0, 1) by fn(x) = x". Show that fn converges to the constant function 0, but that…

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Q: how that fuGe)= x" (1-x") converges bintwise # se G, 1]. Is fn G) Thyenges %3D uni formly?

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Q: Find the radius of convergence, R, and the interval of convergence, I.  infinity signEn=1 xn/n2

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Q: Determine the radius and interval of convergence of F (-1)*(x – 4)k k2k k=1

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Q: Examine the convergence of ,where a>1. (log x)" +1

A: First I have told about Improper integral of first kind and then using it evaluate the given…

Q: {()} Find the rate of convergence of the sequence sin as n=1 n 0 . n n 3 n4 1 n-

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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: Find the interval of convergence : En-0 (x-3)"

A: Apply ratio test to find the interval of convergence. When L<1 then series converges and When…

Q: 04: A) Discuss the convergence of f,(x) =, , on A-(0, 0).

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: 2.1 Show that a sequence of Riemann-Integrable functions fn(r) converges uniformly to a…

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Q: Prove that sina de converges but not absolutely for 0 < p < 1. XP

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Q: Find the interval of convergence of ) n°x" and find its sum. n=1

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Q: (3) Find the radius of convergence of a) infinite b) 1 not defined 0 infinite X Σ₁ F

A: The given series is: ∑j=1∞xjj2 Let, aj=xjj2; j≥1

Q: The interval of convergence of +∞ x2n Σ(-1)" is (2n)! n=0

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

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Q: Check the convergence of J (x-2)²

A: Let x-2=tThen dx=dti.e.∫-∞11(x-2)2dx∫-∞-11t2dt      [x=-∞, t=-∞-2=-∞]  [When x=1, t=1-2=-1]

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

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Q: Analyse the convergence of the sequence {fn} where fu(x) = on R. 1+ na²

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Q: Determine the radius and interval of convergence of (-1)*k!æk (2k + 1)! k=0

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Q: Show that the sequence of functions {f.} where f,(x)=nxe is non-uniformly convergent on [0,1]. (by…

A: Test for uniform convergence of sequences: Let fn be a sequence of functions such that it converges…

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

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Q: 2. Show that following sequence of functions are convergence pointwise to its limit function. a)…

A: See the attachment

Q: Find the interval of convergence of (3x)^n/(2n)!

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Q: Let {fn(x)} x E R and x > 0. 1+ xn use defination of unifrom convergence to Show that the…

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Q: Working directly from the e-N definition of convergence (without using any rules for limits), prove…

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Q: Consider Hhe seguen ce (f,) of funcdions fa:R-R defined by: fn (x) = Cos for 番<x< %3D 2. 2. Discuss…

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Q: Find the radius of convergence of (-1)"x' 4n n=0

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Q: Suppose that p(x) > ana" converges on (-1, 1], find the internal of convergence of p(3x - 7). n=0…

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Q: 8. Prove that lim(x_) = 0 if and only if lim(jx,i) = 0. Give an example to show that the conver-…

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Q: Construct a sequence of continuous functions fn : R →→ R such that 0 < fn S 1, limn-o Jo fndx = 0…

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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: that converges to a function on R ii)show n х 1=0n!

A: For this, we will use the Ratio Test, which can be written for a series ∑n=0∞an as: limn→∞ an+1 an…

Q: 04: Determine the convergence of tan¹(x) x²+n²In(n+2) , on A = [0, +00).

A: We have to determine the convergence of the given series of functions ;   ∑n=1∞an = ∑n=1∞tan-1xx2+n2…

Q: what is b? it is the same question as a, so what is the convergence of B?

A: We can solve this as follows:

Q: 1 i. Use the result in (i) to test for convergence 2n =1 2 Vn? +5

A: See the attachment

Q: Q No 2: a) Discuss the convergence and divergence of (1+ a"), Va eR.

A: We have to divide it into several cases.

Q: 4) Consider the function given by (-1)*+' (x-7)* Ax) = E n =1 Find the interval of %3D convergence…

A: The function is  f(x)=∑n=1∞ (-1)n+1(x-7)nn

Q: Find the interval of convergence of Ln=1 (r-1)" 2n

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Q: 7. Let f(x): Find the interval of convergence of f. (2n+1)!

A: Given series

Q: Define s F: [0,0)-IR, Fa- esinr dy Use Dominated Convergence Theoren ond show that: dF (H= at -1…

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Q: ∞ f(x) = L n=1 (7-2x)" Sn

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