SUMMARY
The limit evaluation of sin(5r)/r as r approaches 0 can be resolved using the substitution method. Specifically, the known limit lim as r->0 of sin(r)/r equals 1 is applicable here. By substituting 5r for r, the limit transforms to lim as r->0 of sin(5r)/(5r) multiplied by 5, resulting in a final limit of 5. This technique is essential for handling similar limits in calculus.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with the limit property lim as x->0 of sin(x)/x = 1
- Basic substitution techniques in mathematical analysis
- Knowledge of trigonometric functions and their behavior near zero
NEXT STEPS
- Study advanced limit evaluation techniques in calculus
- Learn about L'Hôpital's Rule for indeterminate forms
- Explore Taylor series expansions for trigonometric functions
- Investigate applications of limits in real-world scenarios
USEFUL FOR
Students and educators in mathematics, particularly those focusing on calculus, as well as anyone looking to strengthen their understanding of limit evaluation techniques.