Solution:
\( \lim \limits _{x \rightarrow \infty} \frac{ 2x^3+7}{x^3-x^2+x+7} = \lim \limits _{x \rightarrow \infty} \frac{ \frac{2x^3}{x^3}+\frac{7}{x^3}}{\frac{x^3}{x^3}-\frac{x^2}{x^3}+\frac{x}{x^3}+\frac{7}{x^3}} = \lim \limits _{x \rightarrow \infty} \frac{ \frac{2}{1}+\frac{7}{x^3}}{\frac{1}{1}-\frac{1}{x}+\frac{1}{x^2}+\frac{7}{x^3}} = \frac{2+0}{1-0+0+0}=2 \)
