Limit at Infinity of Rational Functions with Numerator Degree Greater Than Denominator

Conditions

• The function is a quotient of two polynomials.
• The degree of the numerator is greater than the degree of the denominator.
• The variable approaches infinity.

Reasoning, step by step

1. Identify the highest power of the variable in the numerator and the denominator.
2. Compare the degrees of the two polynomials.
3. Conclude that if the numerator's degree is higher, the limit is infinity.

Example

For $\lim_{n \to \infty} \frac{2n^3}{n^2 + 3n + 2}$, the numerator has degree 3 and the denominator has degree 2. Since $3 > 2$, the limit is $\infty$.

Common misconceptions

• Assuming that a growing denominator always makes the whole fraction tend to 0.
• Forgetting to expand the denominator before comparing degrees.

Watch the explanation

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