Can Continuity at 0 Guarantee Equality at 0?

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Homework Help Overview

The discussion revolves around a question of continuity in the context of two functions, f and g, specifically examining whether continuity at a point implies equality at that point under certain conditions involving sequences.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster expresses uncertainty about the validity of the statement regarding continuity and equality at zero. Some participants suggest reconsidering the limit as n approaches zero, while others question if the limit should actually be as n approaches infinity.

Discussion Status

Contextual Notes

There is a potential ambiguity in the limits being discussed, as participants are considering different approaches to the sequences defined in the problem statement.

mathmajor2013
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Homework Statement



True or false? If f and g are continuous at 0 and f(1/(2n+7))=g(1/(7-2n)) for all positive integers n, then f(0)=g(0).

Homework Equations



lim x->0 f(x)=f(0)
lim x->0 g(x)=g(0)

The Attempt at a Solution



NO CLUE. My intuition says false.
 
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hi mathmajor2013! :smile:

hint: forget lim x->0 …

what is lim n->0 ? :wink:
 
I'm wondering if tiny-tim didn't mean "[itex]n\to \infty[/itex]"?
 
oops! :rolleyes:
 

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