SUMMARY
The limit of sin(4x)/3x as x approaches 0 can be evaluated using the Squeeze Theorem. The transformation sin(4x)/(4x) approaches 1 as x approaches 0, which is established by the limit u->0 of sin(u)/u=1, where u=4x. Thus, the limit lim (sin(4x)/3x) as x approaches 0 equals 4/3.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with the Squeeze Theorem
- Knowledge of the limit property lim (sin(u)/u) as u approaches 0
- Basic algebraic manipulation skills
NEXT STEPS
- Study the Squeeze Theorem in detail
- Review proofs of the limit lim (sin(u)/u) as u approaches 0
- Practice evaluating limits involving trigonometric functions
- Explore advanced limit techniques in calculus
USEFUL FOR
Students studying calculus, particularly those focusing on limits and trigonometric functions, as well as educators teaching these concepts.