SUMMARY
The limit of (sin 2x)/(sin 5x) as x approaches 0 can be evaluated using the fundamental limit property, lim (sin x)/x = 1. By rewriting the expression, the limit can be transformed into the product of two simpler limits: (sin(2x)/(2x)) and (5x/sin(5x)). This approach leads to the conclusion that the limit evaluates to 2/5.
PREREQUISITES
- Understanding of trigonometric limits, specifically lim (sin x)/x = 1.
- Familiarity with limit notation and evaluation techniques.
- Basic knowledge of algebraic manipulation of expressions.
- Concept of multiplying by a form of one to simplify limits.
NEXT STEPS
- Study the derivation and applications of the limit lim (sin x)/x.
- Explore advanced limit techniques, such as L'Hôpital's Rule.
- Learn about continuity and differentiability in calculus.
- Practice solving various trigonometric limits for deeper understanding.
USEFUL FOR
Students studying calculus, particularly those focusing on limits and trigonometric functions, as well as educators looking for clear examples of limit evaluation techniques.