2 sin x+1 dr 3 -dx +1

Q: •1 2. In r dr

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Q: Series to Rind use lim 1- Cos 2X

A: Use series expansion of the e3x and cos 2x with help of ex and cos x:

Q: th Use the ri"-term test to find wether the fottowing Sexies exe divergent or not- n+2

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Q: sin(n) Q2: Does En=2 convergent or divergent by use integral test? n2

A: Explanation of the answer is as follows

Q: Sinlxy). lnx dx 19141 to be investipa te the uniform Convergence of ne parametric intepral)

A: Given integral is, ∫01sinxylnxxdx Since, the given integral is improper integral so applying the…

Q: Which of the follo wing information is correct for the sequence 3 1 dx 5 1 dx 7 1 dx 1 dx {anin=l ?…

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Q: Detine s F: [o,0)IR, FCH=2 -tx sinx dx Use Dominated Convergence Theoren and show that: dF -1 eand…

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Q: How do I do this one?

A: Given integral is The integral is improper and can be evaluated as follows Since, the value of…

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Given,

Q: e 1

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Q: -2x Determine whether |e*dx is convergent or divergent. If it is convergent state what value the…

A: Given  ∫0∞e-2xdx

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

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

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Q: Evaluate the integral. Does it converge or diverge? x dx

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Q: Determine if convergence or divergence. 4 -dx xln?x |

A: Given that some integration we solve this integration by using general formulas of integration. Here…

Q: ог Question A.) Does this CONVERGE • DIVERGE ? (~) ² M nal

A: To determine whether the given series converges or diverges.∑n=1∞ln n2n

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not…

A: In this question we have to find whether the Integral is divergent or convergent.

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Here this question based on improper integral

Q: A)(sin x)/ is convergent or not B){x} is convergent or not

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Q: Evaluate the integral or state that it diverges. 1 dp. 4 X' - 1 Select the correct choice and, if…

A: Given: The integral ∫01x3x4-1dx

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Topic = Integration

Q: dx Jx +x²

A: Please see the below picture for detailed solution.

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

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Q: .Does 00 sin? (n) 2n n=1 converge or diverge? Use any method and give reasons for your answers.

A: Here for the series we use Dirichlet’s Test:

Q: Which test to use and is it convergent/divergent? 1 Σ Z 16n2 – 8n – 3 n=1

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A: Given the integral,  ∫2∞ 3x+532dx  The functionf(x)=3x+532 is undefined at point x=-5 ,  Since…

Q: y hues of a, 6 >o is the following integeal For which Convergent? x* (1 + x*)

A: According to the given information, it is required to find the values of a,b>0 for which the…

Q: f(t) = 1 – |t| con –T <t < T Determine The half path expansion in terms in sines, analyze the…

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Q: dive ges. If it conve ges, find the Determine whether the seavence converges or n+1o Sin(n) 3n+ 2

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Q: CK Show whye* dx does or does not converge.

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Q: dx Use the fact (1+x)x^; dx = 2 tan" (Vx)+C. You will need to think a little on this one©. 2.…

A: We will use the given indefinite  integral to  check whether the improper  integral given converges…

Q: tan-1 1+n2 n=1

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Q: 2+cosx 1. Use the comparison Theorem to determine whether dx is convergent or divergent

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Q: n.Sin (t Converges or diverger

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Q: A pply Taylor's s expansion and find the se yies for tann at = 4 %3D

A: We need to find Taylor's expansion for tan2x at π4.

Q: da Determine if this integral converges or diverges. If it converges find this value

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

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Q: Find all values of a ER such that the improper integral x" sin? r dr er converges. Show your work.

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Q: e{3k(n +7) sin( 1. -) +7} k(n+7)

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Q: 6. S o Inx dx Evaluate it and state whether it converges or diverges. 1 х2

A: Given: I=∫0∞lnxx2dx

Q: Evaluate this Improper integral: dx (a) Does it converge or diverge? (b) If it converges, to what…

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Q: x² + e-3 dx

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Q: Converge or diverge with what test?

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Q: (b) Let D be a circular domain of radius R with center at the origin. Show that sin(r² + y²) dr dy…

A: We will first transform the coordinates from Cartesian to polar using x= rcos\theta, y= rsin\theta.

Q: Evaluate this Improper integral: X eX dx (a) Does it converge or diverge? (b) If it converges, to…

A: If integration value is finite then it is convergent.

Q: Determine whether the improper integral 6x²-x dx converges or diverges, and find the value if it…

A: To determine whether the improper integral ∫-∞∞ 6x5 e-x6 dx converges or diverges.

Q: me for those converges. 1 dx

A: (b) Given integral is: I=∫01ln xxdx Let ln x=t Then we get, 1xdx=dt x=0⇒t=ln 0=undefinedx=1⇒t=ln 1=0…

Q: etermine if the given is convergent c sin(2 tan-1n – T) Σ (2 tan-1n – Tt) n=1

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Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

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Q: -dx converges ex - e- Select one: O True O False

A: