SUMMARY
The limit of the function (X³ + 3X²)/(X² + 6X + 9) as X approaches -3 is determined to be DNE (Does Not Exist). The initial confusion arose from the calculation yielding 0/0, which is an indeterminate form. Upon further analysis, it was clarified that the denominator approaches 0 while the numerator also approaches 0, confirming the limit does not exist. This discussion highlights the importance of recognizing indeterminate forms in limit evaluations.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with indeterminate forms, specifically 0/0
- Basic algebraic manipulation of polynomials
- Knowledge of evaluating limits using substitution
NEXT STEPS
- Study the concept of indeterminate forms in calculus
- Learn techniques for resolving limits, such as L'Hôpital's Rule
- Explore polynomial long division for limit evaluation
- Practice evaluating limits involving rational functions
USEFUL FOR
Students studying calculus, particularly those focusing on limits and indeterminate forms, as well as educators seeking to clarify these concepts for learners.