I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 2.8 : Limits at Infinity, Part II
9. Evaluate \(\displaystyle \mathop {\lim }\limits_{x \to \,\infty } \ln \left( {\frac{{11 + 8x}}{{{x^3} + 7x}}} \right)\).
Show SolutionFirst notice that,
\[\mathop {\lim }\limits_{x \to \,\infty } \frac{{11 + 8x}}{{{x^3} + 7x}} = 0\]If you aren’t sure about this limit you should go back to the previous section and work some of the examples there to make sure that you can do these kinds of limits.
Also, note that because we are evaluating the limit \(x \to \infty \) it is safe to assume that \(x > 0\) and so we can further say that,
\[\frac{{11 + 8x}}{{{x^3} + 7x}} \to {0^ + }\]Now, recalling Example 5 from this section, we know that because the argument goes to zero from the right in the limit the answer is,
\[\mathop {\lim }\limits_{x \to \,\infty } \ln \left( {\frac{{11 + 8x}}{{{x^3} + 7x}}} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{ - \infty }}\]