Curriculum
General Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
0/10
Unit 2: Exponents, Logarithms and Applications
0/10
Unit 3: Limits
0/6
Unit 4: Trigonometry
0/4
Text lesson
Limits at Infinity
Limits at Infinity
Rational functions at infinity
Rational functions at infinity
- To find the limit of a rational function at ∞, divide the numerator and the denominator by the highest power of x in the denominator, then apply limx → ∞ 1/xn = 0 to each term.
- The degrees (highest powers) of the numerator and the denominator give a quick rule:
| Comparison of degrees | Limit at ∞ |
|---|---|
| Degree of the numerator is less than the degree of the denominator | 0 |
| Degrees are equal | Ratio of the leading coefficients |
| Degree of the numerator is greater than the degree of the denominator | Infinite (∞ or −∞) |
- If limx → ∞ f(x) = L, then the horizontal line y = L is a horizontal asymptote of the graph.
Limits at Infinity · 2 / 5