Solving Limits (Rationalization)

Watch this video on finding limits algebraically. Be warned that removing x-4 from the numerator and denominator in Step 4 of this video is only legal inside this limit. The function \frac{x - 4}{x - 4} is not defined at x = 4 ; however, when x is not 4, it simplifies to 1. Because the limit as x approaches 4 depends only on values of x different from 4, inside that limit \frac{x - 4}{x - 4} and 1 are interchangeable. Outside that limit, they are not! However, this kind of cancellation is a key technique for finding limits of algebraically complicated functions.

Last modified: Monday, October 11, 2021, 3:37 AM