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anonymous
 5 years ago
determine if the integral 1 / (1+x^2)^1/2 converges or diverges (Hint. use comparison test)
so far i compared it to integral 1/ (x^2)^1/2 but that diverges
anonymous
 5 years ago
determine if the integral 1 / (1+x^2)^1/2 converges or diverges (Hint. use comparison test) so far i compared it to integral 1/ (x^2)^1/2 but that diverges

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It diverges. I used the p series test though. If you distribute the exponent of 1/2, you get x^1/2, and 1/2 < 1 so it is divergent. If you are required to use the ratio test, you must use a function that gives values smaller than the original.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm sorry not x^1/2 but it equals 1/x which if you use the integral test goes to the natural log, which is divergent. Also according to the p series test, the degree in the denominator must not equal one, so either way it diverges.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If you need to use the comparison test, you'd compare it to 1/x because in the example you used, you must distribute the exponent.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but its the wrong comparison

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0how do you compare it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i am using the comparison test, so 0< integral g(x) < integral f(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if integral g(x) diverges, then integral f(x) diverges , find integral g(x)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes, the function you choose must be smaller. In this instance, the +1 doesn't matter, giving us 1/(x^2)^1/2, so if you distribute the one half, you get 1/x, which we can is the function g(x). We know g(x) diverges because of the several tests I mentioned above (both the integral, ratio, and p series tests) which means that the function f(x) which is 1/(1+x^2)^1/2, riveted as well. Therefore, because g(x) diverges, so does f(x). Does that answer your question?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0no because 1/x^2 ^1/2 is greater than 1 / ( 1 + x^2 ) ^1/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its in the wrong order

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In this instance it doesn't matter, because if you take the limit as you approach infinity, the +1 doesn't matter. It's like 1/10000000 is hardly different from 1/10000001.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but youre not using the comparison test then

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can check it by the Alternating series test. If it still diverges, it absolutely diverges.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its not an alternating series though

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If there was an x! Or another variable, then it would change things, but a constant is irrelevant in this instance.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know it's not alternating. You use the alternating test to check for absolute divergence or convergence. For example, 1/x is conditionally divergent because if it alternates, it converges. If there is no alternating piece, it diverges. Hence, you can use the alternating test to check if it always diverges or only sometimes.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hmmm, how is that relevant

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It allows you to check convergence or divergence. That was your question originally.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah, this question im getting tutored for im sorry

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i promise i will answer your question

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I'm saying, if you have a choice, I wouldn't use the comparison test. If you don't, then just do the same thing with the denominator that is larger and use one of the methods I discussed earlier to see.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0can yuo give me a formal method

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You mean show you the steps? To which one? The comparison test? The p series? The integral test?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0any , the comparison test fails, as i explained earlier

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the direct integral comparison test

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0cantor can u help me now, I have 2 parts left and I'm done. first question at the top
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