A Concept of Limits by Donald W. Hight

Author:Donald W. Hight
Language: eng
Format: epub
Publisher: Dover Publications

It follows then by the limit definition that sin x = 0.

Example 2 Determine that cos x = 1.

Solution: From statement (2) we have

Also, since 0 < –x < π whenever –π < x < 0, it follows that

But, (–x)2 = x2 and cos (–x) = cosx; thus, (2) and (5) combine to yield

If we knew that , then the domination principle stated in Exercise 7 of §2–12 would imply that cos x = 1. It is your privilege as a participating reader to complete this solution by proving (see Exercise 2).

Example 3 Determine

Solution: We will use the results of Example 2 and statements (1) and (3). Statement (3) was

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