Lecture 5 - Continuous Function

Lecture series on Mathematics-1 by Prof S.K.Ray,
Department of Mathematics and Statistics IIT Kanpur
For more details on NPTEl, visit http://nptel.iitm.ac.in

Category:

Education

Tags:

• Mathematics
• Continuous
• function

[gcruz6875]

Yes, you are right. People who watch this are superior human beings whose curiosity and ambition have made us different from animals like you.

[iqsaleh]

ssashita: you're wrong. Prof.Ray used the sequence definition and delta-epsilon definition to show continuity. You hve cut/paste an elementary US calculus definition which is another definition. As a mathematician, I must say you have erred

[jonhrty]

i'd like to thank you for the very thorough explanation... Also for future videos it'll be great if you write bigger! Thanks

[aslongasiamalive]

it'd be great if you could increase the video quality...the writing is just too strenuous for the eyes.

[MegaJollyboy]

hand writing ....... x

[afrostac]

Thanks for the lectures, it was very useful for me.

[jh8182]

These videos are great except it is not big enough to read. Can you make the writting clearer and bigger?

[rhudaina]

ssashita...I'm sorry but you have study Math more..

[SolosWithStyle]

This really helped, thanks!

[yesilful]

sasita epsilon plus and minus behaves similar to right and left hands limits of the function f(x). they the same things but only the notations used are different from each other.

[ssashita]

Dear Prof. Ray, With due respect to your efforts and scholarship, I think your definition of continuous function has a conceptual error.

 A real function, f(x), is continuous at x=c, if the right and left hand limits of f(x) at x=c and f(c) all exist and (and this is the part you missed) are all equal. You only talk about the limit of f(x) at x=c. We can always define a non-continuous function such that the limit at x=c exists as a finite value, yet is a value different from f(c).