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Question
\[\lim_{x \to \infty} \frac{5 x^3 - 6}{\sqrt{9 + 4 x^6}}\]
Solution
\[\lim_{x \to \infty} \left[ \frac{5 x^3 - 6}{\sqrt{9 + 4 x^6}} \right]\]
\[\text{ Dividing the numerator and the denominator by } x: \]
\[ \lim_{x \to \infty} \left[ \frac{\frac{5 x^3 - 6}{x^3}}{\frac{\sqrt{9 + 4 x^6}}{x^3}} \right]\]
\[ = \lim_{x \to \infty} \left[ \frac{5 - \frac{6}{x^3}}{\sqrt{\frac{9}{x^6} + 4}} \right]\]
\[ = \frac{5}{\sqrt{4}}\]
\[ = \frac{5}{2}\]
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