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
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.
Supplemental Resources (optional)
Lesson: Limit of a Function, Dale Hoffman's Contemporary Calculus