SUMMARY
The limit of sin(cos(x) - 1) / x as x approaches 0 is definitively evaluated to be 0. The solution involves applying L'Hôpital's Rule, which is used to resolve indeterminate forms. An alternative method includes multiplying the expression by (cos(x) - 1) / (cos(x) - 1) to simplify the limit. This approach confirms the result without further complications.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with L'Hôpital's Rule
- Knowledge of trigonometric functions and their properties
- Basic algebraic manipulation skills
NEXT STEPS
- Study L'Hôpital's Rule in depth, including its applications and limitations
- Explore trigonometric limits and their evaluations
- Learn about series expansions for trigonometric functions
- Investigate alternative methods for evaluating limits, such as the epsilon-delta definition
USEFUL FOR
Students and educators in calculus, mathematicians focusing on limit evaluations, and anyone seeking to deepen their understanding of trigonometric limits and L'Hôpital's Rule.
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