anonymous
  • anonymous
Use the Comparison Test to show that the integral, x^a/((x^b)+1) from 1 to infinity, converges if b>a+1
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Use the Comparison test to show that the integral \[ \int\limits_{1}^{\infty}x ^{a}\div x^{b}+1 dx\] converges if \[b> a+1\]
anonymous
  • anonymous
compare it to 1/x^p, where p>1, you know that because b > a+1, your power in the denominator is greater than your power in the numerator, so when you go to evaluate the integral, the lim as x -> infinity for 1/infinity will be 0 which allows it to converge.

Looking for something else?

Not the answer you are looking for? Search for more explanations.