SUMMARY
The limit of the function lim (x-1)/(1-x) as x approaches negative infinity is definitively -1. The correct approach involves recognizing that the constants 1 and -1 become negligible when x is very large in magnitude. By simplifying the expression to x/-x, the limit is clearly established as -1.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with algebraic manipulation of functions
- Knowledge of approaching limits at infinity
- Basic comprehension of rational functions
NEXT STEPS
- Study the concept of limits at infinity in calculus
- Learn about rational function behavior as x approaches infinity
- Explore techniques for simplifying complex fractions
- Review examples of limits involving negative infinity
USEFUL FOR
Students studying calculus, particularly those focusing on limits, and educators looking for clear explanations of limit concepts.