$x \rightarrow \infty$时多项式型函数的极限

\[
\lim_{x \rightarrow \infty} \frac{\sqrt{4x^6-5x^5}-2x^3}{\sqrt[3]{27x^6+8x}} \\
=\lim_{x \rightarrow \infty}\frac{-x^5}{\sqrt[3]{27x^6+8x}(\sqrt{4x^6-5x^5}+2x^3)} \\
= \lim_{x \rightarrow \infty}\frac{-x^5}{(\frac{\sqrt[3]{27x^6+8x}}{\sqrt[3]{27x^6}} \times 3x^2)(\frac{\sqrt{4x^6-5x^5}+2x^3}{4x^3} \times 4x^3)} \\
= \lim_{x \rightarrow \infty}\frac{1}{(\frac{\sqrt[3]{27x^6+8x}}{\sqrt[3]{27x^6}} )(\frac{\sqrt{4x^6-5x^5}+2x^3}{4x^3})} \times \frac{-5x^5}{(3x^2)(4x^3)} \\
= \frac{1}{(\sqrt[3]{1+0})(\sqrt{\frac14+0}+\frac12)} \times \frac{-5}{12} \\
= \frac{-5}{12}
\]