Question: Find

\[\underset{x\to 3}{\mathop{\lim }}\,\frac{2{{x}^{4}}-3{{x}^{3}}-81}{{{x}^{5}}-10{{x}^{3}}+27}=\left( \frac{0}{0} \right)=\underset{x\to 3}{\mathop{\lim }}\,\frac{8{{x}^{3}}-9{{x}^{2}}}{5{{x}^{4}}-30{{x}^{2}}}=\frac{8\times 27-9\times 9}{5\times 81-30\times 9}=1\]

Apply 1’Hopital’s rule as many times as necessary, verifying your results after each application.