In mathematical research, some important and typical problems are often studied and summarized, in the hope that solving these problems will lead to the solution of a series of related problems. The two important limits introduced in this paragraph embody such a By using these ideas and through the identity deformation of functions：and the operation rules of limits, two types of commonly used limit calculation problems can be solved.

　　1.  

　　Proof :  Since is an even function , we only need to discuss the case of .

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　　Construct the unit circle ( see the figure above ) and set the angles

,

The tangent line at point intersects the extension line of at , because

,

so

,

According to the commonly used formula for calculating area , we have

Triangle area sector area triangle area,

There is

,

thereby

,

Organize, get

,

From ( the previous example in this section ) and the pinching criterion , we get

.