a) The improper integral f dx is (Select ] ( Select ] Convergent Divergent None of these b) The improper integral dr is ISerect ) c) The improper integral f e" dx is [ Select] >

Q: (b) Prove that the improper integral Ï Ï -8 -∞ converges. dx dy (1 + x² + y2)3/2

A: Consider the given improper integral, I=∫-∞∞∫-∞∞dxdy1+x2+y232 Change into circular coordinates by…

Q: Determine the convergence or divergence of serie sin Σ 6n2 n +4 n=1

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Q: 5₂00⁰ dx 2 3 1.

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Q: 1. Write the improper integral which is represented by the following limit. lim C2" 2x dx x2-4 2.…

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Q: Determine whether the improper integral (r – 1)3 dr is convergent or divergent.

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Q: Define if the given proper integrals converge or diverges a) 4 1 x2 – 2 b)| 1 -dx 7x2 + 1

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Q: a) dr. A<1

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Q: 1 (a) Use the Integral Test to show that > converges. 2. n' +1 d 1 n = 0 -1 tan dx Hint: 1+x?

A: As per our guidelines, we are supposed to solve only one question.  Kindly post other questions  as…

Q: (b) Check the convergence of the improper integral z1z dr. Z+2

A: Topic- improper integration

Q: Compute the definite integral as the limit of Riemann sums. .2 3) (x2 + x + 1) dx

A: Definite integral

Q: 5. Use the Comparison Theorem to prove whether the integral converges or diverges. 2.x 2.x3 +7

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Q: The integral in this exercise converges. Evaluate the integral without using a table 2 dx 32

A: Given,          ∫-322dx2x

Q: b)does the integral converge 2x-2 dar (r+1)(x²+1

A: Consider the given integral. I=∫1∞2x-2x+1x2+1dx Now, find the partial fraction of the function.…

Q: ∞ e4y dy

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Q: 1. Determine if the infinite integral is convergent or divergent dx x² + 2 - 2

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost the other…

Q: 1 Evaluate the improper integral or show that it is divergent. x In x

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Q: 30. Determine if the integral dx is convergent or divergent c. Neither a. Convergent b. Divergent d.…

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Q: 4. (a) Use the limit definition of improper integrals to evaluate dx (b) Does the improper integral…

A: 4.a. let I = ∫2∞dxx3

Q: Perform a test to determine if it converge or diverge -1 x 2sin 1 dx 1– x -1

A: The function is given by: ∫-112sin-1x1-xdx If the function fx=2sin-1x1-x is positive, continuous and…

Q: Determine the convergence of the integral 2 tan x UTM UTM dx. (In(cos x) GUTM

A: Given: ∫π3π2tanxlncosx2dx

Q: (6) Decide if the following improper integrals are convergent or divergent using Basic Comparison…

A: Calculating convergence of given improper integrals using basic comparision test

Q: 1/8 | x In (8x)dx

A: To find the value of integral substitute 8x=t

Q: 1 Evaluate the integral of ₁dx for P > 1, and determine whether it is convergent or divergent. xP

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Q: 1 Use the Cauchy's integral test to show that Σ diverges n. In n. In In n n=2

A: Cauchy -Integral  Test series ∑n=1∞ an      converges if integral ∫1∞ f(x) dx finite and  diverge if…

Q: 4. (a) Use the limit definition of improper integrals to evaluate dz (b) Does the improper integral…

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Q: Determine the convergence of the integral tan r dx J; (In(cos x))²

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Q: 3. Using the integral test, prove that diverges. n=1 n

A: We have given series ∑n=1∞1n. The integral test states that  The series is ∑n=1∞an is convergent if…

Q: In(1+3y) dx. Utilizando desarrollos limitados, determine la convergencia de la integral cos(x)-1-1

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Q: 1 Determine the convergence of the integral dr. (2-r)

A: To determine convergence of the integral  ∫0512−x13dx

Q: 1. Determine if the infinite integral is convergent or divergent r+oo dx |x² + 2 -00

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Q: 2. Determine the convergence of the improper integral e² In x dx.

A: Take the integral, ∫0∞xlnx=lnxx22-∫0∞1x.x22dx=x2lnx2-x240∞=∞ As after taking x→∞ the limit of the…

Q: 11. Determine the divergence or convergence of the following improper integrals and evaluate if it…

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Q: 1 dx (x – 1)4 18. 3

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Q: An odd piecewise continuous function f(x) on every finite interval of (-0, 0) such that / fx)| dxis…

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Q: 3 , evaluate the improper integral dr. x2 + x – 2 Does it converge or diverge? Justify your claim.

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Q: 1 Use the Integral Test to determine whether the scries is convergent or V3k + 5 k=1 divergent.…

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Q: Only piecewise continuous functions f(x) on every finite interval (0, ∞) such that F(x)| dxis…

A: The given statement is false.

Q: Give an example of a convergent improper p-integral. For the toolbar, press ALT+F10 (PC) or…

A: The answer is found in step-2

Q: 4. Show that the series f(x) = E cos(nx) ni+ 2021 converges uniformly on R. Use this to show that f…

A: given sequence is                                                 we have to check convergence of…

Q: 5. Use Watson's lemma to obtain the first two terms in the asymptotic expansion as x → o of the…

A: Like a function, an integral can also be expanded in its asymptotic series. The conception of this…

Q: Determine the convergence of the integral tan x d.x. E (In(cos r))2

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Q: 1.3 write the fallowing integral (a) e | Determine whether the folawir Converges or diverges. x- 3x°…

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Q: 1. Determine if the following integral converges or diverges. Note that it is improper integral.…

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Q: Evaluate the definite integral: (2 – a²)dx using limit of the Riemann sum.

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Q: Use the definition of the convergence of an improper integral to determine whether the following…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Determine the convergence of the integral tan x UTM &UT dx. (In(cos x))² COS X

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Q: (a) (6) Decide if the following improper integrals are convergent or divergent using Basic…

A: To decide the convergence of the improper integrals.

Q: Only piecewise continuous functionsf (x) on every finite interval (0, 0) such that 00 | S(x)| dxis…

A: According to the condition of convergence for Fourier integral,  Let f and f' be piecewise…