This preview shows page 1. Sign up to view the full content.
Unformatted text preview: A Transition to Advanced Mathematics by Smith, et.al (7 th ed.) Clarification/Hints for 1.3 Exercise 12 Note: solutions to such a problem can vary. Let R + = R > = { x R : x > } . (12a) As stated in book. From calculus, write the symbolic form for the definition of f is continuous at a . (12a) Clarified statement of (12a). Let f : R R be a function. Let a R . Write a symbolic form of the definition of f is continuous at a . (12a) A solution. Let f : R R be a function. Let a R . Then, by definition, f is continuous at a precisely when: for each > 0 there exists > 0 such that if  x a  < then  f ( x ) f ( a )  < . Thus the definition of f is continuous at a can symbolically be written as: ( R + ) ( R + ) ( x R ) [  x a  <  f ( x ) f ( a )  < ] . By years of convention, it can also be written as: ( > 0) ( > 0) ( x R ) [  x a  <  f ( x ) f ( a...
View Full
Document
 Fall '11
 Staff
 Calculus, Advanced Math

Click to edit the document details