Limit of \( \displaystyle \frac{36 x^{2} - 1}{18 x^{2} + 3 x} \) as \( x \to \infty \)

Problem 1.304 · medium

1. \[ \lim_{x \to \infty}\left(\frac{36 x^{2} - 1}{18 x^{2} + 3 x}\right) \]
   limit algebraStart with the limit of the given function as x approaches infinity. Divide the numerator and denominator by x**2.✓ Proved
2. \[ = \lim_{x \to \infty}\left(\frac{36 - \frac{1}{x^{2}}}{18 + \frac{3}{x}}\right) \]
   simplifySimplify the terms inside the limit.✓ Proved
3. \[ = \lim_{x \to \infty}\left(36 - \frac{1}{x^{2}}\right) \left(\lim_{x \to \infty}\left(18 + \frac{3}{x}\right)\right)^{-1} \]
   limit-lawApply the quotient rule for limits.✓ Proved
4. \[ = 2 \]
   limit simplifyEvaluate the limits of the numerator and denominator separately. Simplify the resulting fraction.✓ Proved