SUMMARY
The limit of the expression (x^2 - 1) / |x - 1| as x approaches 1 from the right is 2, while from the left it is -2. This indicates that the limit does not exist at x = 1 due to the differing values approached from either side. The calculations confirm that the right-hand limit yields a positive result, whereas the left-hand limit results in a negative value, establishing a clear discontinuity at this point.
PREREQUISITES
- Understanding of limits in calculus
- Knowledge of absolute value functions
- Familiarity with one-sided limits
- Basic algebraic manipulation skills
NEXT STEPS
- Study the concept of one-sided limits in calculus
- Explore the properties of absolute value functions
- Learn about discontinuities and their classifications
- Practice solving limits involving piecewise functions
USEFUL FOR
Students studying calculus, particularly those focusing on limits and continuity, as well as educators looking for examples of limit behavior around discontinuities.