Additional Reference Limits and Special Cases

This page continues the exploration of reference limits, focusing on more specific cases and providing additional examples relevant to 30 limites de fonctions Exercices corrigés PDF and Tableau des limites usuelles.

The page is structured around limits as x approaches zero, both from the positive and negative sides. It also includes some special cases that are particularly important for understanding function behavior.

Example: lim(x→0) 1/x = +∞ (for x > 0) demonstrates the behavior of the reciprocal function near zero.

One of the key limits presented is the natural logarithm as x approaches zero:

Highlight: lim(x→0+) ln(x) = -∞, showing that the natural logarithm approaches negative infinity as x gets arbitrarily close to zero from the positive side.

The page also covers the limit of x * e^x as x approaches zero, which is an important result often used in calculus:

Definition: lim(x→0) x * e^x = 0, known as an indeterminate form that resolves to zero.

This information is crucial for students working on Limite 0 et 0 problems and preparing for advanced calculus courses.

Vocabulary: Indeterminate form refers to a limit expression that doesn't have an immediately obvious value and requires further analysis.

The content on this page complements the previous page, providing a more complete picture of Tableau limite de fonction quotient and other important limits. Together, these pages form a comprehensive guide for students studying limits in advanced mathematics courses.