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The Calculus Lifesaver by Adrian Banner

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CHAPTER 14 _____________________________

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.

14.1 L’Hôpital’s Rule

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 ...

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