Math · Calculus

Introduction to Limits

Learn what a limit means before working with formal rules and formulas.

Introduction to Limits

Video coming soon for this lesson.

Objectives

  • Understand the intuitive idea of a limit as approach.
  • Interpret what happens to f(x) as x approaches a value.
  • Recognize basic limit notation.

Introduction

A limit describes what value a function approaches when the input gets close to a point.

Basic idea

A limit describes the behavior of a function near a point.

Worked example

Find the limit of f(x)=x+3f(x)=x+3 as x approaches 2.

  1. 1Look at the function f(x)=x+3f(x)=x+3.
  2. 2See what happens when x approaches 2.
  3. 3Then f(x) approaches 5.
The limit is 5.

Practice

1. What does a limit describe?

It describes what value a function approaches.

Common mistake

Assuming that computing a limit always means direct substitution.

Summary

  • A limit describes approach.
  • We observe what happens to f(x) as x approaches a value.
  • Limits are foundational in calculus.

Quick quiz

1. What does a limit represent?
  • The largest value of a function.
  • The behavior of a function near a point.
  • The slope of a line.

The behavior of a function near a point.