Predicting the behavior of rational functions as they approach infinity
In short: When a fraction's numerator and denominator both grow without bound, how do we determine the final result? This video breaks down the three general cases for limits at infinity.
Sal Khan analyzes three different rational functions to categorize how their limits behave as inputs approach infinity. By identifying these patterns, students can predict whether a function stabilizes at a specific value, grows indefinitely, or approaches zero.
The lesson is part of the AP Calculus AB curriculum and was developed with input from Bill Scott, who uses Khan Academy to teach at Phillips Academy in Andover, Massachusetts.
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Sources
- Summary by Intellect · source: Limits at infinity of quotients (Part 2) | Limits and continuity | AP Calculus AB | Khan Academy
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