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S = contains supplemental resources
Course: Calculus II
Topic: Calculus of Infinity
Subtopic: Indeterminate Forms and L'Hopital's Rule

Overview

We know that zero divided by a non-zero number is zero, and that a non-zero number divided by zero is "undefined", but what about zero divided by zero? We know that 0^1=0 and that 1^0=1, but what about 0^0? Things like 0/0 or 0^0 are called indeterminate forms because they are not necessarily determinable. We will look at them in terms of limits, such as lim(x/sin(x)) as x->0 (which appears to approach 0/0).

Early in Calculus I we studied various approaches to evaluating limits (worth reviewing now!) including those of the form 0/0. We attacked them using algebra to rewrite or simplify the function. But a nice alternative is to use L'Hopital's Rule. This rule can be used to evaluate limits of the form 0/0 or ∞/∞.

Objectives

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

• 9.1.1 Recognize the four "special limits" from Calculus I and how to evaluate them
• 9.1.2 Recognize determinate forms and indeterminate forms
• 9.1.3 Understand when L'Hopital's Rule applies to a limit and when it does not
• 9.1.4 Transform indeterminate forms so that L'Hopital's Rule applies (including using the "ln method" as appropriate
• 9.1.5 Evaluate a limit using L'Hopital's Rule once or repeatedly

Terminology

Define: the four "special limits", determinate form, indeterminate form, L'Hopital's Rule, the "ln method"

Supplemental Resources (optional)