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Question

Evaluate the limit to infinity
$lim x \to \infty \frac{{3 x}^{3} - {4 x}^{2} + 6 x - 1}{{z x}^{3} + x^{2} - 5 x + 7} = \frac{3}{2}$

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Solution

$lim x \to \infty \frac{3 x^{3} - 4 x^{2} + 6 x - 1}{2 x^{3} + x^{2} - 5 x + 7}$

$= lim x \to \infty \frac{x^{3} (3 - \frac{4}{x} + \frac{6}{x^{2}} - \frac{1}{x^{3}})}{x^{3} (2 + \frac{1}{x} - \frac{5}{x^{2}} + \frac{7}{x^{3}})}$

$= \frac{3}{2}$

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