3. Show that the improper integral x*e*dx is convergent and gives the answer of 4! (It turns out that r"e*dx = n!, and this is one way to extend the factorial function to other real numbers. ) You might use the tabular method to find the antiderivative

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

A: The given integral is ∫0∞dxx2

Q: The improper integral -dx is (x+2)® 1 converges to O Diverges converges to converges to converges to…

A: ∫-1∞1x+295dx=∫-1∞x+2-95dx                                =-541x+245-1∞…

Q: In S₁² = 10 A (1,00) B (-∞0,00) c) (-∞,1] D {0,1} Given -dx, determine all value/values of P for…

A:

Q: 2- Find the values of p for which integral converges. dz z(ln z)

A:

Q: 1 Determine if the integral [Inxdx converges or diverges. 0

A: Given problem:- Determine if the integral ∫01ln(x)dxconverges or diverges

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

A:

Q: a) dr. A<1

A:

Q: Find the values of p for which the integral converges. (Enter your answer as ar '1 1 9. хр (-∞<p<1)U

A: evaluate the integral and find what values of p the answer does not exist

Q: The improper integral de x+4x+8 converges to converges to * converges to O None diverges

A: Put (X+2) = t and expand

Q: The improper integral 1 xp- (x + 4)4 is convergent. Select one: True O False

A: To solve this question we need to apply the concept of convergence and divergence of improper…

Q: Given a > 0, the improper integralJa ran-ix(1+x³)' dx is convergent to In- In if: a = 1 a = 2 O the…

A:

Q: 1 The improper integral -dx x²+2x+5 O None O diverges converges to 3n converges to converges to

A: Solution:To find the integral ∫1∞1x2+2x+5dxFormula:∫1x2+a2dx=1atan-1xa+C

Q: Evaluate the improper integral f 5( x – 4)² dx ; if your integral converges state 3 what value it…

A: You have posted multiple questions. As per the instruction, we will be answering only the first one.…

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

A:

Q: Show that integral 0 to infinity e -x 2 is convergent.

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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

A:

Q: Evaluate the integrals that converge 32 1 dx 2 ㅇ x5

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The improper integral dx 2 x2+4x+8 converges to 4 O None converges to 37 converges to O diverges

A: Topic- integration

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

A:

Q: (b) Prove that the improper integral ]] 8888 converges. dr dy (1 + x² + y2)3/2

A: Solution: Given improper integral, ∫-∞∞∫-∞∞dxdy1+x2+y232 As we know the convergence of the series is…

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: In(x84 dx The integral converges to 0 converges to -336 goes to co дoes to -oo converges to 336

A:

Q: 1. Evaluate the following Improper Integral. Does the limit converge? Why or why not? [Apply the…

A: According to our guidelines we can only provide solution of one problem at a time, therefore i have…

Q: 8. 1 9. V.x-1

A: We use the definition of convergence of improper integrals to check whether the given improper…

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

A:

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

A:

Q: 6. The improper integral 1 dx converges to х -5 попe 2 1 4

A: We have to find

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…

A:

Q: Determine whether the improper integral ∞∫−∞dxx2+2x+8 converges or diverges?

A:

Q: What is the radius of convergence from > Vn (x – 1)" n=0

A: Given power series is ∑n=0∞nx-1n The given power series converges if…

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: 3. Determine if the assigned improper integral is convergent or divergent. Lever e²+1 dr

A: Given problem:-

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: dx

A:

Q: In some cases, it is impossible to fin d the exact value of an improper integral, but it is…

A:

Q: The improper integral dx is (x+2)8 1 O None converges to Diverges 5 converges to converges to 5…

A:

Q: Evaluate the indefinite integral 3x dx = (x + 8)² 3x dx ---Select--- Converges The integral (x + 8)²…

A:

Q: 2. Use the Comparison Theorem to determine whether the integral x +4 J. V-2-1 dx x4 – 2x – 7…

A: Comparison Test for integrals: If fx≥gx≥0 on the interval [ a, ∞), then, 1. If ∫a∞fxdx converges,…

Q: 2. Determine if the integral converges or diverges. Part of your grade on this problem depends on…

A: Topic:- integration

Q: Evaluate the improper integral and state whether it converges or diverges.

A: Definite integral convergence

Q: (b) Explain why the integral e- *x* dx is convergent.

A:

Q: 00 dz (7x – 2)8

A: We need to evaluate the given integral-

Q: Find the radius of convergence for: – 1)"x" Σ Vn + 5 n n=1

A:

Q: b. Si x-2ª 3 1

A: ∫13dxx-2    =  [ lnx-2 ]13   =  ln|3 - 2| - ln|1 - 2| =  ln |1| - ln |-1|   =  0 - 0  = 0

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.