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The Calculus Lifesaver by Adrian Banner

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CHAPTER 3 ______________________________

Introduction to Limits

Calculus wouldn’t exist without the concept of limits. This means that we are going to spend a lot of time looking at them. It turns out that it’s pretty tricky to define a limit properly, but you can get an intuitive understanding of limits even without going into the gory details. This will be enough to tackle differentiation and integration. So, this chapter contains only the intuitive version; check out Appendix A for the formal version. All in all, here’s what we’ll look at in this chapter:

• an intuitive idea of what a limit is;

• left-hand, right-hand, and two-sided limits, and limits at ∞ and −∞;

• when limits fail to exist; and

• the sandwich principle (also known as the ...

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