SUMMARY
The limit as x approaches 0 of the expression (1/(2+x) - 1/2)/x simplifies to -1/4 without using L'Hôpital's rule. The discussion highlights the use of partial fractions to simplify the expression effectively. The key steps involve rewriting the limit as [1/(2+x) - 1/2] / x and further simplifying it to -1/(2x+4). The final result confirms that as x approaches 0, the limit converges to -1/4.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with partial fraction decomposition
- Basic algebraic manipulation skills
- Knowledge of approaching limits without L'Hôpital's rule
NEXT STEPS
- Study the concept of limits in calculus, focusing on indeterminate forms
- Learn about partial fraction decomposition techniques in algebra
- Explore alternative methods for evaluating limits without L'Hôpital's rule
- Practice solving similar limit problems to reinforce understanding
USEFUL FOR
Students studying calculus, mathematics educators, and anyone interested in mastering limit evaluation techniques.