Limit of \( \displaystyle \frac{15 x - 7}{9 x + 4} \) as \( x \to \infty \)

Problem 1.107 · medium

1. \[ \lim_{x \to \infty}\left(\frac{15 x - 7}{9 x + 4}\right) \]
   limitStart with the original limit expression.✓ Proved
2. \[ = \lim_{x \to \infty}\left(\frac{15 - \frac{7}{x}}{9 + \frac{4}{x}}\right) \]
   algebra simplifyDivide both numerator and denominator by x. Simplify the fractions inside the limit.✓ Proved
3. \[ = \lim_{x \to \infty}\left(15 - \frac{7}{x}\right) \left(\lim_{x \to \infty}\left(9 + \frac{4}{x}\right)\right)^{-1} \]
   limit-lawApply the quotient rule for limits.✓ Proved
4. \[ = \lim_{x \to \infty} 15 \left(\lim_{x \to \infty} 9\right)^{-1} \]
   limitEvaluate the limits of the individual terms.✓ Proved
5. \[ = \frac{5}{3} \]
   simplify simplifyPerform the division. Reduce the fraction to lowest terms.✓ Proved