0o Inx dx Evaluate it and state whether it converges or diverges. x2 d)

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: The improper integral 2e dx is: -00 (a)converge to 2 (b) converge to - 2 (c) converge to 0 (d)…

A: In this question we have to define the integral.

Q: 1) Does cos" cn) Sin*™(n) converges uniturmly on D, : [0, K14] ?. And on

A: Given sequence of function is, fnx=cosnxsin2nx. It can be written as, fnx=cosxsin2xn. If common…

Q: nst. . Decide whether the fo lowing is convergent In the con ver or ०१en1 ९ase ८a्रlवnee ५e 6+1)4"+…

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Q: Let f and g be as in the figure, we may deduce that if I g(x)dx converges then

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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: 1 f(2) = zexp(iz?) + 1+ 2iz (b) Find its radius of convergence.

A: Given function is fz=zexpiz2+11+2iz We have to find the radius of convergence of the given function.…

Q: (x + n)² Show that h„(x) converges poimtwise to f(x) = 1, V x e [1, 00). %3| x² + n²

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

A: Consider the given series

Q: The improper integral | 2e*dx is: -00 (a)converge to 2 (b) converge to – 2 (c) converge to 0 (d)…

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Q: 00 The improper integral 2e*dx is: -00 (a)converge to 2 (b) converge to – 2 (c) converge to 0 (d)…

A: We need to evaluate the following integral ∫-∞∞2exdx

Q: 1.₂0 +00 1 2. Determine whether the integral da converges or rvin x diverges. If it converges,…

A: We have to find out integral

Q: 1002+x dx Then I J = 1 None of these converges to 1 converges to 2 converges to 3 O is divergent

A: Given I = ∫1∞ 2+xx3dx = ∫1∞(2x-3+x-2) dx = 2∫1∞x-3dx + ∫1∞x-2dx2x-2-21∞ + x-1-11∞= -1x21∞+ -1x1∞=…

Q: dx converges and, if so, to what. 49. Determine whether J = | E/1* I-

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

A: Divergent test: If

Q: MEDI is a) converges to 2 b) converges to 2/2 c) converges to 23 d) diverges e) None of all

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

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Q: Let r be a constant. Suppose >,r i=1 converges to 8, then the sum of >r' is i=0 Answer:

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

A: The given series is

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

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Q: dx Jx +x²

A: Please see the below picture for detailed solution.

Q: Determine i it convergcs or dverges. Evaloate if converges oo dv 2.

A: We have given,

Q: 15) Determine whether the integral is divergent or convergent. If convergent, evawate. If not state…

A: Topic = Integration

Q: The improper integral 2e*dx is: (a)converge to 2 (b) converge to – 2 (c) converge to 0 (d) diverge

A: To solve the given improper integral.

Q: 1 d.x x In (ex)

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Q: The improper integral 2e dx is: 514 (a)converge to 2 (b) converge to - 2 (c) converge to 0 (d)…

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Q: dx Determine if the improper interal S, xc Fnd it valne if it converges. Conneeges on diree jes.…

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Q: 4. Based on the definition, the integral Sx'dx. Choose an option below and explain why. -0o a. Is…

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Q: . Determine whether I = dx converges or diverges. If it converges, find its value. %3D r5/2

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Q: Determine if H conver or diverges. Evaluate i it ges converges dx 3

A: We have to find convergence and divergence of integral .Integral is shown as below:

Q: Determine whether r{(1+E)*"}.. Converges or diverges.

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Q: Let 1 = S dx c+∞ 4-x I = dx Then I O converges to 3 O converges to .

A: Consider the integral: I=∫1+∞4-xx3dx

Q: dX Show that Xe* converges/diverges.

A: Given : an  = 1 / x e(x)^2

Q: d 23 a Show that dx :(-{e-*(sin x + cos x) ) = e¬* sin x. N. 00 b Find e* sin x dx, and show that…

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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: Determine whether or not the infinite series below converges.

A: Here the given series is

Q: dx too - can you deduce about Vx* +2x+6 ct one: a. it is convergent b. converges to 1 c. diverges d.…

A: The given integral

Q: The following improper integral dx Vx2-1 diverges to +o converges to V15 This option O This option…

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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: dx The improper integral git + x^ Diverges Converges

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Q: Let p > 0. Consider the following improper integrals. 1. Show that dz converges if and only if p <…

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Q: tó úsé co ór -0o, enter INFINITY or -INFINITY, respectively.) (-1)" + 1n! 1. 8. 15 ... (7n + 1) n =…

A: Given- ∑n=0∞(-1)n+1n!1.8.15....(7n+1) We have to determine the convergence or divergence of the…

Q: 07)Fmd the that converges And dotam COs

A: Consider the given function whose Laurent series is required to calculate.

Q: メー) whatis theradius h.gh of convergense f the power senes) 9.3 b. 2

A: ∑n=1∞(x-1)nn.3nwe have to find radius of convergence of the power series

Q: Σ-(, n=1 n7/2 Put 'C' below if the integral converges, or 'D' if it diverges.

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Q: dx is convergent a) true b) false O b

A: The given integral is: ∫1∞1x2dx To find it is convergent or divergent. The integral is convergent if…

Q: Perform a test to determine if dx converges or diverges. - 0o Vx° +6

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Q: 11. Let I = SÄ In(4x) dx. Then a. I converges to 0 1 b. I converges to 4 c. I is divergent

A: Substitute 4x = t, so 4dx = dt dx=dt4 And when x = 0, t = 0 and when x = 1/4, t = 1.…

Q: SELEC A) converges B) diverges C) D)

A: The given series is: ∑n=2∞1n3-n

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

A: