SUMMARY
The limit of the expression (t^2 - 9)/(t - 3) as t approaches 3 can be evaluated by factoring the numerator into (t - 3)(t + 3) and canceling the (t - 3) terms. This cancellation is valid because the limit process allows for the assumption that (t - 3) is not equal to zero as t approaches 3. Substituting t = 3 into the simplified expression yields a limit of 6.
PREREQUISITES
- Understanding of limits in calculus
- Ability to factor polynomial expressions
- Knowledge of substitution methods in limit evaluation
- Familiarity with the concept of indeterminate forms
NEXT STEPS
- Study the concept of limits approaching indeterminate forms
- Learn about L'Hôpital's Rule for evaluating limits
- Explore polynomial long division for more complex limits
- Practice additional limit problems involving factoring and substitution
USEFUL FOR
Students studying calculus, particularly those focusing on limits and polynomial functions, as well as educators seeking to reinforce these concepts in their teaching.