Determine if the following converges or diverges as x approaches infinity by either evalutation, the direct comparison test, or the limit comparison test: (It's a Calculus II, AP Calculus BC level of problem)(adsbygoogle = window.adsbygoogle || []).push({});

the integral of (lnx/(square root of (x^2-1))), from 1 to infinity.

* I do not know how to evaluate the integral analytically, so I tried to use either the direct comparison test or limit comparison test. I can't seem to find another function that will "sandwich" that function (and thus prove convergency) or one that will prove it's divergency. I've tried 1/x, 1/(x^2), etc and I'm stuck. Any help on a function to use would be very much appreciated- I'm frustrated beyond belief!

Direct Comparison Test:

0< f(x)< g(x) proves that f(x) converges if g(x) also converges

f(x)> g(x)---proves that f(x) diverges if g(x) diverges

Limit Comparison Test:

if the limit as x approaches infinity of f(x)/g(x) is a finite, non-zero number, then f(x) has the same behavior of convergence as g(x)

**Physics Forums - The Fusion of Science and Community**

# Determine if the following converges or diverges

Know someone interested in this topic? Share a link to this question via email,
Google+,
Twitter, or
Facebook

- Similar discussions for: Determine if the following converges or diverges

Loading...

**Physics Forums - The Fusion of Science and Community**