Whenever a limit contains a rational expression in \(n\), first compare the degrees of the numerator and denominator.
• If the degrees are equal, the limit is the ratio of the leading coefficients.
• If the numerator has a smaller degree, the limit is \(0\).
• If the numerator has a larger degree, the limit is \(\infty\) (or \(-\infty\), depending on the sign).
Dividing by the highest power of the variable is the quickest and most reliable method.