SUMMARY
The limit of ln(x)/x as x approaches 0 from the right is evaluated as an indeterminate form of type -∞/0. The correct approach involves recognizing that as x approaches 0, ln(x) approaches -∞ while x remains positive, leading to the conclusion that the limit diverges to -∞. This analysis confirms that the limit does not yield a finite value but rather indicates the behavior of the function near the specified point.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with logarithmic functions
- Knowledge of indeterminate forms
- Basic algebraic manipulation skills
NEXT STEPS
- Study the properties of logarithmic limits
- Learn about L'Hôpital's Rule for resolving indeterminate forms
- Explore the behavior of functions approaching infinity
- Practice evaluating limits of other logarithmic expressions
USEFUL FOR
Students studying calculus, mathematics educators, and anyone seeking to understand the behavior of logarithmic functions near critical points.
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