SUMMARY
The limit of Sin x/|x| as x approaches 0 exists and is equal to 1. This conclusion is reached by evaluating the limit from both sides of 0, specifically by analyzing the behavior of the function as x approaches 0 from the positive and negative directions. The approach involves substituting small values, such as 0.001 and -0.001, to confirm that both limits converge to the same value. The critical requirement for the limit's existence is satisfied as both one-sided limits yield identical results.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with the sine function and its properties
- Knowledge of absolute value functions
- Experience with evaluating one-sided limits
NEXT STEPS
- Study the properties of limits involving trigonometric functions
- Learn about one-sided limits and their significance in calculus
- Explore the concept of continuity and its relation to limits
- Practice evaluating limits using numerical substitution techniques
USEFUL FOR
Students of calculus, mathematics educators, and anyone interested in understanding the behavior of limits involving trigonometric functions.