Question 3 Is the given statement true or false? Justify your answer. 'If f is continuous, decreasing function on [1, 00) and lim f(r) = 0, then f(x) da is convergent.' %3D

Q: Question 4. (a) Find the limit: lim z*in(÷). (b) Does the following improper integral exist and…

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

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

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Q: dæ x-1 1

A: Solution: The objective is to find whether the given integral converges or not

Q: QUESTION 13 Is this true or false? The radius of convergence for 00 ΣΕ" n=0 is R = Show why your…

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Q: Question 7 Find the interval of convergence for > (-1)* (k + 3)x* a) O(-0, 0) b) O(-6, 6) с) О(-9,…

A: We have to find interval of convergence.

Q: Question 5 Given f(x) = |2 – 2|. 1) At which points is f not differentiable? Prove your claim using…

A: The function f(x)=2x-2, then we have to answer the following... Solution (1): Since at 2x-2=0⇒x=1,…

Q: 1 E(-1)"+1, ( n + 1 ) . 3η n=1

A: To find whether converges or diverges

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

A: We have to determine whether  ∫-2o{1/(x+1)2 }dx  is convergent or divergent.  Let I =  ∫-2o{1/(x+1)2…

Q: Question 1 Determine the radius of convergence of E(x-6)" n=0 n! med weth CamScanner

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Q: If the sequence of functions {f} converges in measure to two functions f(x) and g(x), then these…

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Q: The graph of a function is shown. AY (a) Does f(x) have a limit at x = a, as x approaches a? O Yes O…

A: a) When we use limit x=a means that the value of x is approch to value of a. Hence x approaches a…

Q: 1 -dx xln*x 1.

A: To determine if the following is a convergent or divergent. ∫e∞1xln4xdx Solution: A indefinite…

Q: Suppose to solve for a root of f(x), i.e., ƒ(x*) = 0, we use the iteration Xk+1 = ¢(xk) where o(x)…

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Q: 2) is E=1 2n convergent?

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Q: If lim =c>0 , then b, , a, both convergent and both divergent.

A: By limit ratio test we know that if above condition is true then either both series diverges and…

Q: (d) T(x - 1)2 can be written in the form |(2 – 1) ' B (e) If f is continuous on [0, o0) and lim f(r)…

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Q: Example 2.3.16 Determine the following integrals are convergent or divergent 8 for e-2x dx

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Q: 1 3 .5 4 X +x

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Q: Determine if  ∫3-2(1/x^3)dx  is convergent or divergent.

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Q: Does sin () x 7 converge or diverge? Why?

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Q: 4. Determine whether the function g(x) = roo sin²x converges or diverges by comparing it to f(x)…

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Q: If the function f is continuous on [0,00) and | f(x)dx is convergent, then there is a possibility…

A: If the function fIs continuous on [0, ∞) and ∫1∞f(x)dx is covergent, then there  is a possiblility…

Q: Are there any values of x for which E=1(1/nx) converges? Give reasons for your answer.

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Q: Determine whether

A: Solution: Consider the given integral equation: J = ∫-11dxx1/3 Since the given integrand is defined…

Q: Question 15: Suppose that the function f(r) is continuous at a ER and (rn) is a se- quence in dom(f)…

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Q: e-n E(-1)"+1 2. п(п + 1) n=1

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Q: Question 3 Find the interval of convergence for (k + 2)! (x – 3)* а) О(-0о, о) b) O {3} с) О (2,4)…

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Q: QUESTION 13 Is this true or false? The radius of convergence for Σ()" n=0 is R = Show why your…

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Q: True or false: Let a function f(x) be continuous, positive, decreasing for all æ > 0, and f(x) → +o,…

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Q: Determine whether E1(-1)" sin n3 is absolute convergent, conditionally convergent, or %=D1…

A: We have to find the series test

Q: Question (2x)" Find the interval of convergence I for n n=1 Give your answer in interval notation.

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Q: (b) Consider the sequence of functions {fn(x)} defined by, sin(nx + 3) Vn +1 fn(x) = , x € R (i)…

A: Solution (b): The sequence of functions fnx is defined by fnx=sinnx+3n+1,x∈ℝ

Q: If lim=c>0, then both convergent and both divergent. ylgn O Ihi O

A: If limn→∞anbn=c>0, then ∑bn,  ∑an both convergent and both divergent. (a) True (b) false

Q: 2. Use the MVT to show • Prove that the derivative of f(x) = k, on [a, b], where k is constant, is…

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Q: ca, is convergent. is an convergent and c is a nonzero constant, then If n=1 n=1

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Q: fn (x) = e-na", E = [1, 0)

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Q: Is the given statement true or false? Radius of convergence of the function f(x)=ex is 1 .

A: False Solution  written below

Q: IV. Determine if the given is convergent or divergent. 1. dx (x2 + 1)² 1

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Q: ÷ + (금)'+ (금)" + (능)' + (금)' + (우) 1 2 3 (1) 1 + 9 (우) Convergent, and the value Check one.…

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Q: ple 5.11.4. If 1 =1+ 1 log n In 1 1 Yn =1+ 2 1 + .+ log n, then prove that {xn} is monotone…

A: We are given xn=1+12+13+.................+1n-logn                and yn=1+12+13+.......+1n-1-logn We…

Q: 1 [3] b) Determine whether dx converges or diverges. Justify your answer 1+x?

A: According to the question, we have to determine whether ∫0∞11+x2 dx converges or diverges. If the…

Q: dx heorem 1.7.1 is convergent if and only if µ < 1. (x – a)H a

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Q: 11 dx Determine whether is convergent or not. (3 – x)2/3

A: As the value of Integral is finite, it converges.

Q: Question 6. Let n + sin nx fn(x) = 3n + sin? nx for x E R. (a) Find the limit function f(x)…

A: Given that fnx=n+sin nx3n+sin2nx   for x∈ℝ (a) The limit function fx=limn→∞fnx…

Q: Question 6 (-1)*k! (x – 1)* Σ (k + 3)3 Find the interval of convergence for

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Q: 2) Calculate each of the limits by considering logarithm of the limit first. a) lim x'n x x→0+ b)…

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Q: +00 1 dx xln*(ex) 4 e

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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…

Q: (B) Let {fn(x)}1 = {r ln x. cos(x – 1)"} be a sequence of meaurable functions defined over [1,2].…

A: