Calculus I -eek 1

Limits and Continuity

This lesson introduces limits, one-sided limits, and continuity.

Big Idea

A limit describes what a function approaches as x gets close to a value. The function does not always need to be defined at that exact value.

Key Example

Evaluate the limit as x approaches 2 of (x^2 - 4) / (x - 2). If you plug in x = 2 directly, you get 0 / 0. That means we simplify first. x^2 - 4 = (x - 2)(x + 2) After canceling (x - 2), the expression becomes x + 2. Now plug in x = 2. 2 + 2 = 4

What You Should Know

- limit is about what a function approaches. - / 0 usually means simplify first. -actoring is often useful in limit problems. -ontinuity means the graph has no break at that point.