SUMMARY
The limit of the absolute value function as x approaches negative infinity is evaluated as follows: \(\lim_{x\rightarrow -\infty}|x| = \lim_{x\rightarrow -\infty} -x\). As x becomes increasingly negative, the value of -x approaches positive infinity. Therefore, the conclusion is that \(\lim_{x\rightarrow -\infty}|x| = +\infty\).
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with absolute value functions
- Knowledge of graphing functions
- Basic algebraic manipulation
NEXT STEPS
- Study the properties of limits in calculus
- Explore the behavior of absolute value functions in different contexts
- Learn about one-sided limits and their applications
- Investigate the concept of infinity in mathematical analysis
USEFUL FOR
Students studying calculus, mathematics educators, and anyone seeking to understand the behavior of absolute value functions at infinity.