SUMMARY
The limit of the function f(x) = sin(x)/x^2 as x approaches 0 is an indeterminate form of 0/0. To resolve this, one must apply l'Hôpital's rule or recognize the limit of sin(x)/x, which equals 1 as x approaches 0. Thus, the limit can be rewritten as lim (x → 0) (sin(x)/x) * (1/x), leading to the conclusion that the limit does not exist due to the divergence of 1/x as x approaches 0.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with the function sin(x)
- Knowledge of l'Hôpital's rule
- Basic algebraic manipulation of limits
NEXT STEPS
- Study the application of l'Hôpital's rule in various limit problems
- Explore the Taylor series expansion for sin(x)
- Learn about the concept of indeterminate forms in calculus
- Investigate the behavior of functions approaching infinity
USEFUL FOR
Students studying calculus, particularly those focusing on limits and indeterminate forms, as well as educators looking to clarify concepts related to trigonometric limits.