## Calculus (3rd Edition)

Since the denominator is non zero at $x=3$, then L’Hôpital’s Rule does not apply. We can find the limit directly as follows $$\lim _{x \rightarrow 3} \frac{2 x^{2}-5 x-3}{x-4}=\frac{2 (9)-5 (3)-3}{3-4}=\frac{0}{-1}=0.$$