{au, ) IL x y² dx dy Q4-A) Show that the sequence B) Evaluate : ah (sinn)}, +sinh( converges to (1).

Q: sin N 8) Show that converges/diverges.

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Q: (f) Assume that g(x) > bna" is convergent on (-R, R). Instead of assuming that f(rn) = 0 assume that…

A: We will prove the part (f) using two theorems   Theorem (a)Let f(x)=∑anxn be a non-constant power…

Q: an a) Converges n2 b) lim an =0 > cans converges dd) > cos (an) Converges n=1 e) Cos can) diverges

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Q: The bounded interval of the following sequence ( where n is natural number *:) is 2 sin?(3n)

A: According to the given information it is required to find the bounded interval of the following…

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

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Q: Let the function g be defined by g(x) = (x^6 + 2)/7. Use the Fixed-Point Theorem to show that the…

A: This question is basically based on the theorem named Banach fixed point Theorem which states that:…

Q: WNII sin 2 7) Show that 4 VN converges/diverges.

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Q: 04: A) Consider the sequence (f,(x) of functions f,:R→R defined by: f.x)=Cos"(x) for-a/25xSa/2.…

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Q: Determine whether the sequence converges or diverges. If it converges, find the limit. (2n-1)!] a)…

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Q: Show that f"(0) = 0. Use induction and the ideas from the above to show that f(k)(0) = 0 for every k…

A: Given that fx=∑n=0∞anxn in the interval -R,R. Then R is the radius of convergence of the function f.…

Q: 1.) Prove that the sequence An= nt n In (2+1) converges to O. That is, prove limln (^+1)=0 nyo

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Q: sin sin A) converges B) diverges

A: Recall: Telescoping Series Test:      Telescoping series are of the form…

Q: B){(sin(x))/x

A:

Q: We consider f: R → R by f(x) = x²-3x. From Calculus, it is known that of (a) = 2x-3. We'll compute…

A: we know, forward difference ∆f(x)=f(x0+h)-f(x0) where h is equal interval of spacing   and symmetric…

Q: Prove that the sequence xn has a convergent subsequence. 3n4 sin n – 4n cos n2 + 2 a) Xn 5n4 – 8n –…

A: We have to prove that xn has a convergent subsequence in each of the given cases.

Q: sin In(n) A) diverges B) converges 8-1

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Q: Given ſtan xdx = limn→∞ Σ-1 (tan 7)) (7) identify if it is a right k=1 Riemann sum. O True O False

A: The right Riemann sum of integral

Q: 00 Let r be a constant. Suppose ' converges to -1, then the sum of )r' is i-1 i-0

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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: Q3) The sequence a, = 1 - (0.2)" a) converges to 0 b) diverges c) converges to e d) converges to 1

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Q: 1) In order to use the integral test, we must verify that the sequence is decreasing (and positive…

A: We have to test series is convergent or divergent

Q: Suppose that the sequence {an} converges to a and that la| < 1. Prove that the sequence {(an)"}…

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Q: Example :- In each of the frollowing, find the radius af Convergence e and interval of somuengent.…

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Q: does the sequence an converge or diverge? Find the limit if the sequence is convergent…

A: givenan=cos(3pi2 - 6n)

Q: value of for which Are there cmy value f converges.

A: We know that a series is said to be convergent if the sequence of its partial sums converges. Using…

Q: 5. LO2 Camille can obtain a residential mortgage loan from a bank at 8.75% compounded semiannually…

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Q: Is the statement always, sometimes or never true? Briefly explain in words. (-1)"a, converges, then…

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Q: I En=1 an converges then 2a, converges.

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Q: k* for some constant k". Lp.) Show that L(po)

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Q: c) Determine if the sequence b, sin(2an + 5) converges or diverges.

A: To determine whether the sequence converges or diverges.

Q: Determine whether the sequence is convergent or divergent. If it is convergent, find its limit. a)…

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Q: COs converge diverge? or

A: