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
katieb
  • katieb
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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.

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