Limit of \( \displaystyle \frac{27 x^{2} + 1}{9 x^{2} - 4} \) as \( x \to \infty \)

Problem 1.104 · medium

1. \[ \lim_{x \to \infty}\left(\frac{27 x^{2} + 1}{9 x^{2} - 4}\right) \]
   limit algebraStart with the limit definition. Divide numerator and denominator by x**2.✓ Proved
2. \[ = \lim_{x \to \infty}\left(\frac{27 + \frac{1}{x^{2}}}{9 - \frac{4}{x^{2}}}\right) \]
   algebraSimplify the fractions.✓ Proved
3. \[ = \lim_{x \to \infty} 3 \]
   limit simplifyEvaluate the limit of each term as x approaches infinity. Simplify the fraction.✓ Proved
4. \[ = 3 \]
   simplifyFinal result.✓ Proved