59. Show that 1- sin x dx converges. x? 00

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

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Q: Answer "True" or "False" for the following: The integral / dx converges.

A: The given integral is ∫0∞dxx2

Q: 1 dx is convergent True False

A: Definite integration

Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

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Q: use the Comparison Test to determine whether the improper integral converges or diverges.

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Q: (6.6] Determine whether the following integral is convergent or divergent. If it is 10 convergent,…

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Q: If 2 a, is convergent with positive terms n=1 is it true that sin (a,) is also n=1 convergent?…

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Q: 6. Determine whether each of the following integrals converges. If so, find its value. (a) x In(x)…

A: Given, ∫1∞xln(x)dx

Q: 6. Is the following improper integral convergent? There is no need to compute the answer, but you…

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Q: 20. Show that if E-1a, converges, then 1 + sin(a,) Σ n=1 converges.

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Q: 00 Determine whether the improper integral ²+37+1 e dx converges or diverges. Show all your steps.

A: Since there is infinity in the upper bound, this is improper integral of type 1.   To evaluate an…

Q: ctoo The improper integral I' dx converges for p<-1. True False

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Q: Determine whether or not the infinite series below converges.

A: Divergent test: If

Q: dX 2) Show that ? Xe converges/diverges.

A: SOLUTION-

Q: 1 n4 + sin“ n=1

A: To find that the given deries diverges or converges

Q: 1 x + ex 2 g dx

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Q: 1 dx is convergent True 8

A: Solution is given as below:

Q: 2. Evaluate the following improper integral if exists (converges). •2 1 dx (x – 2)3/5

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

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Q: use the Comparison Test to determine whether or not the integral converges.

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Q: Use the previous item to determine if the improper integr 2x – x3 | dx (х — 1)2(г2 + 1) converges or…

A: Given that ∫-∞02x-x3x-12x2+1dxSolution…

Q: Determine whether

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

Q: In the given equation as follows , determine whether the statement is true or false. If it is false,…

A: Given that, ∫0∞eax dx converges for a&lt;0 The above statement is true.

Q: use the Comparison Test to determine whether or not the integral converges.

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Q: A. Below, determine whether or not the integrals are convergent: 1. t-²e'dt 2. et cos tdt

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Q: 6 Jlgul sin (nx +3) 1,(x) =- is convergent point wise to zero function. n-1 ylgn O Ihi O

A: Calculate limn→∞fn:  limn→∞fn=limn→∞sinnx+3n-1             =0

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

A: As the mention in above given question when x goes towards infinte than function f(x) gives 0. It…

Q: Use the Comparison Theorem to de x + 1 36 dx Ji O convergent O divergent 8

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Q: 2x Check whether the improper integral / -dx converges (x²+2)² or not.

A: Given : Improper integral ∫-∞∞2xx2+22dx To find : Check whether given integral converges or not.…

Q: Determine whether integral 0 to pie /2 sec x dx    converges or diverges

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Q: 4. Which comparison would show that dx converges? x + e*

A: According to the given information, it is required to tell which comparison would show that the…

Q: use the Comparison Test to determine whether or not the integral converges.

A: To check convergence/divergence of:

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: 3 9x Determine if the improper integral | dx converges or diverges. If it (²-9) converges evaluate…

A: Solution:- solve the integral

Q: b) Determine whether the improper integral 1+ sin x 1+ x2 converges or diverges.

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Q: Check whether the improper integral 2x dx converges or not. (12+1)

A: Thanks for the question :)And your upvote will be really appreciable ;) It converges

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(x)…

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Q: 2. If Exn and E yn are convergent. Show that E(xn + Yn) is convergent.

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Q: 1 -dx x In*(ex) 1. e

A: Topic = Integration If the limit exists and is a finite number, we say the improper integral…

Q: The improper integral | 1 (x+2)6 dx is converges to 5 3 converges to 5 Diverges O None converges to…

A: We have to solve

Q: diverges: too e -2 dx 2. Evaluate the integral and state whether it converges or

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Q: .2 x+15 dx Jx* +3 1

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Q: For what values of p does the integral dx is convergent ( p > 0 ).

A: Here we have to find the value of p for which ∫1∞1xpdx is convergent.

Q: o Inx 2. For p>1, is S, dx convergent? 1 xP

A: It is the improper integral of first kind , limit of integration is infinity. There is so many test,…

Q: 1 dx xln* (ex)

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Q: 55. Show that dx J+4 converges by comparing with x³ + xdx. -3 dx. х

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Q: Show that for every 0 <p <1 the integral sin dr is both improper and convergent.

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Q: Determine if each of the following improper integrals converge or diverge. If it converges, to what?…

A: Here we have to check the convergence of integral.

Q: Suppose that f e C(R) and that | If(x)|dx converges. Show then that 2 f(x)| sin nx|dx sx)dx. lim n00

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Q: Does fn converges to L1 and L2 i.e the distance between fn and f goes to 0

A: By the theorem: A metric  on BE is the uniform metric du  . A sequence of bounded functions fn:E→ℝ…