6. Prove or disprove. (a) Let f2- (: € C:1< J:| < 2). Then there is a sequence of polynomials that converges uniformly to f(s)= (b) Let lal < 1. If S(e) = Then -.

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A: To prove that the relation between the limits of the two given sequences

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A:

Q: (-1)" +1 (3x)" What are all of the values of x , such that * converges? n=1 .1 1 3 .3 X>0 .4 x> 3

A: Applying Root test for the series, the problem is solved

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A:

Q: Let fn RR be a sequence of continuous functions which converg uniformly to a function f : R → R. Let…

A: see my solution

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A:

Q: Let =-7 and I+(3, +4) for all integers n2 1. (a) Show that xnS 2 for all n. (b) Show that (x,} Is an…

A: All proofs are easily only  a) proved using induction  b) proved using definition c) find using a…

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Q: 1 Let {fn} bes sequence of real nonnegative functions on R', consider the following four statements:…

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Q: Determine of each point convergens or diverges: (-2)"(x-3)" (3) √(n+1) M=O

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Q: Suppose that f is a bounded non-negative measurable function. Show that there exists a decreasing…

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A: Any real sequence Xn is said to be convergent if Xn converging to a unique real number. That is, if…

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A: According to the given problem we have to do only two parts of our choice So we select Ist and third

Q: з Σ (-1)^ hai боu итиеть n ди

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Q: Prove {an} is decreasing for n >>1, if ao=1 an

A: A sequence {an} is said to be decreasing when we have  an+1-an&lt;0

Q: (5) Let' (1) : r² + 7x + 12. S(z) dr (a) Use a comparison test to show that. A B converges. S(x) (b)…

A: Introduction: An improper integration is an integration where the integrand is undefined in one of…

Q: (3) If {f} converges uniformly converges uniformly on [a, b]. on (a, b) and {fn(a)} and {fn(b)}…

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Q: 9. Let (x) and (y) be two sequences converges to c with x y for all n. Assume that f is defined for…

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Q: Let fn(x) = x/(n^2+x^2) for x ∈ R. Show that the sequence {fn} converges uniformly to the function…

A: Solution:  Let  fn(x)=xx2+n2,for  x∈ℝ   and  n∈ℕ For  x=0, we  have  fn(0)=0⇒limn→∞ fn(0)=0⇒limn→∞…

Q: Se ทะเ Ifu ^^ +2 2

A: To find whether the series is absolutely convergent or not.

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A: Sol

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.