L’Hôpital’s Rule and Overview of Limits
We’ve used limits to find derivatives. Now we’ll turn things upside-down and use derivatives to find limits, by way of a nice technique called l’Hôpital’s Rule. After looking at various varieties of the rule, we’ll give a summary, followed by an overview of all the methods we’ve used so far to evaluate limits. So, we’ll look at:
• l’Hôpital’s Rule, and four types of limits which naturally lead to using the rule; and
• a summary of limit techniques from earlier chapters.
Most of the limits we’ve looked at are naturally in one of the following forms:
Sometimes you can just substitute x = a and evaluate the limit directly, effectively using the ...