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 2.9 : Continuity
11. Determine where the following function is discontinuous.
\[y\left( x \right) = \frac{x}{{7 - {{\bf{e}}^{2x + 3}}}}\]As noted in the hint for this problem when dealing with a rational expression in which both the numerator and denominator are continuous (as we have here since the numerator is a polynomial and the denominator is a sum of two continuous functions) the only points in which the rational expression will be discontinuous will be where we have division by zero.
Therefore, all we need to do is determine where the denominator is zero and that is fairly easy for this problem.
\[7 - {{\bf{e}}^{2x + 3}} = 0\hspace{0.25in} \to \hspace{0.25in}{{\bf{e}}^{2x + 3}} = 7\hspace{0.25in} \to \hspace{0.25in}2x + 3 = \ln \left( 7 \right)\hspace{0.25in} \Rightarrow \hspace{0.25in}x = \frac{1}{2}\left( {\ln \left( 7 \right) - 3} \right) = - 0.5270\]The function will therefore be discontinuous at : \(x = \frac{1}{2}\left( {\ln \left( 7 \right) - 3} \right) = - 0.5270\).