\begin{align*}
&\lim_{n\to\infty} \frac{9n^3 + 28n^2 + 3n - 5}{17n^3 + 1000n}\\
= &\lim_{n\to\infty} \frac{n^3 (9 + \frac{28}{n} + \frac{3}{n^2} - \frac{5}{n^3})}{n^3(17 + \frac{1000}{n^2})}\\
= &\lim_{n\to\infty} \frac{9 + \frac{28}{n} + \frac{3}{n^2} - \frac{5}{n^3}}{17 + \frac{1000}{n^2}}\\
= &\frac{9 + \lim_{n\to\infty} \frac{28}{n} + \lim_{n\to\infty} \frac{3}{n^2} - \lim_{n\to\infty} \frac{5}{n^3}}{17 + \lim_{n\to\infty} \frac{1000}{n^2}}\\
= &\frac{9}{17}
\end{align*}
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