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Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
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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:

Terminology

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

Supplemental Resources (optional)

Video: Indeterminate Forms and L'Hopital's Rule, Selwyn Hollis's Video Calculus

Lesson: L'Hopital's Rule, Dale Hoffman's Contemporary Calculus