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The Calculus Lifesaver by Adrian Banner

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CHAPTER 4 ______________________________

How to Solve Limit Problems Involving Polynomials

In the previous chapter, we looked at limits from a mostly conceptual view-point. Now it’s time to see some of the techniques used to evaluate limits. For the moment, we’ll concentrate on limits involving polynomials; later on we’ll see how to deal with trig functions, exponentials, and logarithms. As we’ll see in the next chapter, differentiation involves taking limits of ratios, so most of our focus will be on this type of limit.

When you’re taking the limit of a ratio of two polynomials, it’s really important to notice where the limit is being taken. In particular, the techniques for dealing with x → ∞ and xa (for some finite a) are completely different. ...

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