Page 3: Finite and Infinite Limits as x Approaches Infinity
This page covers the behavior of functions as x approaches infinity, discussing both finite and infinite limits in this context.
For finite limits as x approaches infinity, the notation is:
lim f(x) = l
x→∞
Definition: A function has a finite limit at infinity if its values approach a specific number l as x grows arbitrarily large.
Highlight: When a function has a finite limit at infinity, the line y = l becomes a horizontal asymptote of the function.
The page then moves on to infinite limits as x approaches infinity, using the notation:
lim f(x) = +∞ or lim f(x) = -∞
x→∞ x→∞
Vocabulary: Limite che tende a infinito esercizi svolti refers to solved exercises involving limits as x approaches infinity, which are crucial for understanding this concept.
The page provides examples of different scenarios, including limits approaching positive infinity, negative infinity, and cases where the limit depends on the direction of approach (x→+∞ or x→-∞).
Example: lim √(x) = +∞ as x→+∞, demonstrating that the square root function grows without bound as x increases.
x→+∞