1.5 The Limit of a Function

Finding Limits using Graphs:

Finding Limits using Tables:

One-Sided Limits

One-Sided Limits:

Example

The limit exists if and only if “left” limit = “right” limit

Example where limit does not exist: “Jump” behavior As x → 2: Left limit? Right limit?

Example where limit does not exist: undefined behavior near 0

(When x approaches a number, f(x) approaches infinity) Infinite Limits (When x approaches a number, f(x) approaches infinity)

(x approaches infinity, f(x) approaches a finite limit L, or infinity) Limits at Infinity (x approaches infinity, f(x) approaches a finite limit L, or infinity)

Examples:

Examples: