Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
Topic: Limits and Continuity
Subtopic: Limits Numerically

Overview

In this lesson we evaluate limits numerically, i.e. via tables of data representing the function's inputs and outputs. We analyze the data looking for patterns that enable us to make conclusions about limits of the function as x approaches specific input values. Several interesting examples of varying difficulty will be posted for discussion in class. Check them out!

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 1.2.1 Numerically determine the limit of a function when the limit is a real number
• 1.2.2 Numerically determine the limit of a function when the limit is a infinite
• 1.2.3 Numerically determine that a limit of a function does not exist

Terminology

Terms you should be able to define: table of data, numerical analysis

Text Notes

• When evaluating a limit numerically tables of function data are sometimes given and sometimes must be generated electronically. Be sure you are able to produce data tables using your calculator, graphing software, or MS Excel (or equivalent office program).
• One-sided limits are often introduced from a graphical or numerical approach early on in a calculus course with their more formal algebraic evaluation covered later. At this time you should be able to evaluate a one-side limit "by observation" given the graph of the function or a table of data points.

Mini-Lectures and Examples

Supplemental Resources (optional)

rev. 2020-09-21