Find the value of the following limit.
![\[ \lim_{x \to 3} \frac{x^2 - 4x + 3}{2x^2 - 13x + 21}. \]](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-950eacd408ae2bbe70f77aa3f67dc4d5_l3.png "Rendered by QuickLaTeX.com")
We apply L’Hopital’s rule,
![\begin{align*} \lim_{x \to 3} \frac{x^2 - 4x + 3}{2x^2 - 13x + 21} &= \lim_{x \to 3} \frac{2x - 4}{4x - 13} \\[9pt] &= -2. \end{align*}](https://www.stumblingrobot.com/wp-content/ql-cache/quicklatex.com-537c142227ca6ca267b8d181426c0bb9_l3.png "Rendered by QuickLaTeX.com")
Since this limit exists, the application of L’Hopital’s was justified.
Find the value of the following limit.
We apply L’Hopital’s rule,
Since this limit exists, the application of L’Hopital’s was justified.