SUMMARY
The limit of ln(x²-9) approaches -∞ as x approaches 3 from the right (x > 3) because the expression inside the logarithm, x²-9, approaches 0, leading to the logarithm of a number approaching 0, which results in -∞. The user initially miscalculated by evaluating values too close to 3 from the left instead of the right. Correct evaluations using x=3.01 and x=3.001 confirm the limit behavior. This demonstrates the importance of understanding one-sided limits in calculus.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with logarithmic functions
- Knowledge of one-sided limits
- Basic algebra for evaluating expressions
NEXT STEPS
- Study one-sided limits in calculus
- Explore properties of logarithmic functions
- Practice evaluating limits with different functions
- Learn about continuity and discontinuity in functions
USEFUL FOR
Students studying calculus, educators teaching limit concepts, and anyone seeking to deepen their understanding of logarithmic behavior near critical points.