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The Calculus Lifesaver by Adrian Banner

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CHAPTER 7 ______________________________

Trig Limits and Derivatives

So far, most of our limits and derivatives have involved only polynomials or poly-type functions. Now let’s expand our horizons by looking at trig functions. In particular, we’ll focus on the following topics:

• the behavior of trig functions at small, large, and other argument values;

• derivatives of trig functions; and

• simple harmonic motion.

7.1 Limits Involving Trig Functions

Consider the following two limits:

Images

They look almost the same. The only difference is that the first limit is taken as x → 0 while the second is taken as x → ∞. What a difference, though! As we’ll ...

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