00 47. xe? ex² dx -00 -00

Q: •1 2. In r dr

A:

Q: The integral Jo x°dx converges when a < 0 True False

A: Given integral is ∫0∞xαdx with α≤0 we check the value of integral for α≤0

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

A: We need to evaluate :

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

A:

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

A: If f(x)≥g(x)≥0 on the interval [a,∞) then, If ∫a∞f(x)dx converges then so does∫a∞g(x)dx. If…

Q: (x--1)dx Vx6-64

A: Given integral  ∫2∞ x2-1x6-64 dx

Q: Determine whether the doubly infinite improper integral converges and, if so, evaluate it.

A: ∫-∞∞x dx1+x2

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

A: Given integral I=∫3∞xe-x2dx

Q: 2.) xe" dx 8.

A: Given query is to find integral converges or diverges.

Q: Determine if the improper integral, 73 dx, converges converges or diverges.

A: the integral is improper since 0 is a point of infinite discontinuity of the integrand.The integrand…

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

A: Given integral to evaluate ∫-∞11x2+1dx If ∫tbfxdx exists for every t&lt;b then,…

Q: Determine whether the doubly infinite improper integral converges and, if so, evalute it dx (2²+6)/2

A: ................(1) substitute  take derivative put all values in equation 1

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

A:

Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent. arctan(x)…

A:

Q: 2 + e* 43–48 Use the Comparison Theorem to determine whether the 44. integral is convergent or…

A: Explanation of the answer is as follows

Q: Determine whether improper integral converges or diverges, and find the value of each that…

A: The given integral ∫0∞2e-2xdx can be evaluated as, ∫0∞2e-2xdx=2e-2x-20∞…

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

A:

Q: 星() ()y点r

A: We will use the bounded convergence method to show that the given integral is convergent.

Q: Determine whether the improper integral converges or diverges. If converges, find the value. In (x*)…

A:

Q: Determine whether the doubly infinite improper integral converges and, if so, evaluate it.

A: Determine whether ∫-∞∞exdx converges.   A double infinite integral converges if ∫-∞∞fxdx is finite.…

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

A:

Q: Use the Comparison Theorem to determine if the following integral converges or diverges. x2 х* — 2

A:

Q: 4 xP x9-

A: We will find the value of intergral. If the value is finite then this improper integral would be…

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

A: Given the integral         ∫-∞192x-32dx. Determine whether the integral is divergent or convergent.

Q: Determine if the improper integral converges or the integral. diverges. If it converges, evaluate dz…

A: Calculate the improper integral of the given integration. The integration is given as: ∫−2∞ 14+z22dz

Q: Determine whether the following integrals converge or diverge.

A:

Q: 1/x ,2 xp -0-

A:

Q: 38. Determine whether the following improper integral is con- vergent or divergent, and find its…

A: ∫-∞0x3e-x4 dx Consider, ∫x3e-x4 dx Put, x4=t⇒4x3=dtdx⇒x3 dx=dt4 Therefore, ∫x3e-x4 dx=∫e-t…

Q: da Determine if the following integral converges? 3- 2x

A:

Q: Which of these improper integrals is convergent? e dz 1 eda e*dx 3 -dr 3 -dr 3 8 8

A:

Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the…

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

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

A: The given improper integral is ∫8∞xe-2xdx. The improper integral ∫8∞xe-2xdx can be rewritten as…

Q: Determine if the following improper integral converges or di- verges. If it converges, find the…

A: As per the guidelines only one question should be solved. Thus repost the second different question…

Q: The integral converges; I = }.

A: The integral converges when I=13. We have to give an example.

Q: Determine whether the following Improper integral converges or diverges. If it converges then…

A: Given that

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

A:

Q: Calculate dx, Also state whether The integral converges or diverges, and in the latter cose, ifit…

A: Consider the given integral ∫e∞1xlnx2dx

Q: ex Figure out whether the improper integral dx is J_1 (1-e*)2 convergent or divergent. If it…

A:

Q: Determine whether the following integrals converge or diverge. If they converge, find the value of…

A:

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

A:

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

A: Given: ∫-∞152x-32dx

Q: Determine whether the improper integral converges or diverges. If converges, find the value. In x?dx

A:

Q: Evaluate the following improper integrals. Tell whether it is convergent or divergent. 1.

A: The given integral,     ∫1+∞dxx

Q: Determine if the following integral is convergent or not. x – 1 dx Vr5 + 2 1

A:

Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. So e VE dæ…

A:

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

A:

Q: Determine whether the following integrals are convergent or divergent. If convergent, evaluate its…

A: To evaluate I=∫-∞0xex2dx

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

A: Given: ∫-∞132x-32dx The given query is to find integral converges or diverges.

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.