Page 281 - Calculus Workbook For Dummies

Chapter 14

Ten Things about Limits, Continuity,

andInfinite Series

In This Chapter

When limits, continuity, and derivatives don’t exist
Ten tests for convergence

n this very short chapter, I give you two great mnemonics for memorizing a great deal
Iabout limits, continuity, derivatives, and infinite series. If I do say so myself, you’re get-
ting a lot of bang for your buck here.

The 33333 Mnemonic

This mnemonic is a memory aid for limits, continuity, and derivatives. First, note that I’ve put
the word “limil” under the five threes. That’s “limit” with the t changed to an l. Also note the
nice parallel between “limil” and the second mnemonic in this chapter, the 13231 mnemonic —
in both cases, you’ve got two pairs surrounding a single letter or number in the center.

3 3 3 3 3

l i m i l

First 3 over the “l”: 3 parts to the definition
of a limit

You can find the formal definition of a limit in Chapter 3. This mnemonic helps you remember
that it’s got three parts. And — take my word for it — just that is usually enough to help you
remember what the three parts are. Try it.