Unformatted text preview: c ∈ [0 , 1] such that f ( c ) = c . This c is called a ﬁxed point for f . [Hint: consider g ( x ) = f ( x )x and investigate the endpoints.] (6) Is f ( x ) = x 2 uniformly continuous on R ? Is it uniformly continuous on (0 , 1)? Show why or why not. (7) Use the ±δ deﬁnition to show that f ( x ) = x 3 is continuous at all points in R ....
View
Full
Document
This note was uploaded on 02/09/2012 for the course MATH 410 taught by Professor Staff during the Summer '08 term at Maryland.
 Summer '08
 staff
 Natural Numbers, Mathematical Induction

Click to edit the document details