SUMMARY
The limit value of the expression \(\mathop {\lim }\limits_{\theta \to 0} \left( {\frac{{\ln \left( {1 + \sin \theta } \right)}}{{\sin \theta }}} \right)\) is definitively 1. This conclusion is reached using L'Hôpital's Rule, which is applicable in this scenario due to the indeterminate form encountered as \(\theta\) approaches 0. Participants in the discussion confirmed this result, affirming the correctness of the solution.
PREREQUISITES
- Understanding of L'Hôpital's Rule
- Knowledge of limits in calculus
- Familiarity with logarithmic functions
- Basic trigonometric functions, specifically sine
NEXT STEPS
- Study the application of L'Hôpital's Rule in various limit problems
- Explore the properties of logarithmic functions in calculus
- Investigate other indeterminate forms and their resolutions
- Practice solving limits involving trigonometric functions
USEFUL FOR
Students studying calculus, particularly those focusing on limits and L'Hôpital's Rule, as well as educators seeking to clarify these concepts for their learners.