# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sun, 26 May 2013 03:21:36 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: analysis question for limits of functionsPosted: Wed, 19 Nov 2008 06:01:33 UTC
 Member

Joined: Sat, 15 Nov 2008 06:23:03 UTC
Posts: 18
I have this statement:

If f does not have a limit at c, then there exists a sequence s(n) in D with each s(n)≠c such that s(n) converges to c, but (f(s(n)) is divergent.

I know that it is true but not quite sure how to justify my answer. It is obvious that if f doesn't have a limit at c then it diverges -- but how to show that the sequence of that function diverges?

Top

 Post subject: Posted: Wed, 19 Nov 2008 22:28:44 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
First of all what are all these things you're asking about? What are and ? There may not be such a sequence in general, say . Then cannot possibly have a limit at since we cannot get arbitrarily close to it. But there's no sequence where such that when .

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous