Problem 34

We say that a function is squeezed at if there exist functions and such that for all in an open interval containing , and

 

The Squeeze Theorem states that in this case,  

Step 1.

Let be given. We may choose  such that

if , then and .

A different may be required to obtain the two inequalities for and , but we may choose the smaller of the two deltas. Thus,

if , we have

 

and