The second page delves deeper into comparison theorems and introduces function composition concepts with practical applications.

Definition: The sandwich theorem (théorème des gendarmes) states that if f(x) ≤ g(x) ≤ h(x) and the limits of f and h are equal, then g has the same limit.

Example: For g(x) = 5-cos(x)/$x²+4$, using the fact that -1 ≤ cos(x) ≤ 1, we can determine its limit.

Highlight: The page emphasizes the importance of comparing growth rates of different functions when analyzing limits.

Vocabulary: Croissances comparées refers to the comparison of growth rates between different functions.

The final page focuses on asymptotes and methods for finding them in function graphs.

Definition: An asymptote is a line that a curve approaches indefinitely without ever reaching it.

Highlight: Two main types of asymptotes are discussed: vertical asymptotes (when x approaches a number) and horizontal asymptotes (when y approaches a number).

Example: To find a vertical asymptote, prove that lim f(x) = ∞ as x approaches a specific value.

Vocabulary: Asymptote verticale (vertical asymptote) and asymptote horizontale (horizontal asymptote) are key terms in analyzing function behavior at extreme values.

This page introduces fundamental concepts of function limits and comparison theorems in mathematical analysis. The content focuses on reference functions and their limiting behavior.

Definition: A limit describes the value that a function approaches as the input approaches a particular value or infinity.

Example: For function g(x) = 1+3/2x, the limit approaches 1 as x approaches infinity.

Highlight: The comparison theorem states that if g(x) ≤ f(x) for all x in interval I, and lim f(x) = +∞, then lim g(x) = +∞.

Vocabulary: Reference functions (fonctions de référence) are standard functions whose limiting behavior is well-known and used as benchmarks.