For each of the following integrals, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition. (To indicate convergence or divergence, enter one of the words converges or diverges in the appropriate answer blanks.) ₁2314212 de a similar integrand is 2z Sidr a similar integrand is 3152212 dza similar integrand is ₁3 de a similar integrand is so we predict the integral so we predict the integral converges so we predict the integral diverges so we predict the integral diverges

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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I know I can plug in the infinity into the integrand like plug it in into limits, but I do not understand the first part. Please explain and answer this question, thank you!

 

For each of the following integrals, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges.
Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition.
(To indicate convergence or divergence, enter one of the words converges or diverges in the appropriate answer blanks.)
z²+1
z3+42+2
e2x
3:2
z+2
1731522+2
S
5,00
1
da a similar integrand is
dự
dx a similar integrand is
dx a similar integrand is
a similar integrand is
5,00 da:
x+3
so we predict the integral|
so we predict the integral converges
so we predict the integral diverges
so we predict the integral diverges
Transcribed Image Text:For each of the following integrals, give a power or simple exponential function that if integrated on a similar infinite domain will have the same convergence or divergence behavior as the given integral, and use that to predict whether the integral converges or diverges. Note that for this problem we are not formally applying the comparison test; we are simply looking at the behavior of the integrals to build intuition. (To indicate convergence or divergence, enter one of the words converges or diverges in the appropriate answer blanks.) z²+1 z3+42+2 e2x 3:2 z+2 1731522+2 S 5,00 1 da a similar integrand is dự dx a similar integrand is dx a similar integrand is a similar integrand is 5,00 da: x+3 so we predict the integral| so we predict the integral converges so we predict the integral diverges so we predict the integral diverges
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