## Trigonometric functions.

Proposition 4.5.6

(i)

(ii)

(iii)

The following proposition has a nice geometric proof, using the sandwich theorem (later on, 6.1). A more efficient way to prove it is to use either L'Hopital's rule ( i.e. Theorem L'Hopital) or MacLaurin polynomials (v.i. def Taylor polynomial); we will learn them later.

Proposition 4.5.7

(i)

(ii)

(iii)

Example 4.5.8   Let . Compute the limit, if it exists, of for arbitrary close to 0.

As , we have:

Note that there are other ways to solve this question; one of them will appear in chapter 6, section section l'hopital, another one in chapter 10, section v6.

Noah Dana-Picard 2007-12-28