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 2.4 : Limit Properties
7. Use the limit properties given in this section to compute the following limit. At each step clearly indicate the property being used. If it is not possible to compute any of the limits clearly explain why not.
\[\mathop {\lim }\limits_{x \to \, - 5} \frac{{x + 7}}{{{x^2} + 3x - 10}}\]Okay, at this point let’s step back a minute. We used property 4 here and we know that we can only do that if the limit of the denominator is not zero. So, let’s check that out and see what we get.
\[\begin{alignat*}{3}\mathop {\lim }\limits_{x \to \, - 5} \left( {{x^2} + 3x - 10} \right) & = \mathop {\lim }\limits_{x \to \, - 5} {x^2} + \mathop {\lim }\limits_{x \to \, - 5} 3x - \mathop {\lim }\limits_{x \to \, - 5} 10 & & \hspace{0.25in}{\mbox{Property 2}}\\ & = \mathop {\lim }\limits_{x \to \, - 5} {x^2} + 3\mathop {\lim }\limits_{x \to \, - 5} x - \mathop {\lim }\limits_{x \to \, - 5} 10 & & \hspace{0.25in}{\mbox{Property 1}}\\ & = {\left( { - 5} \right)^2} + 3\left( { - 5} \right) - 10 & & \hspace{0.25in}{\mbox{Properties 7, 8, & 9}}\\ & = 0 & & & \end{alignat*}\]So, the limit of the denominator is zero so we couldn’t use property 4 in this case. Therefore, we cannot do this limit at this point (note that it will be possible to do this limit after the next section).