Proving the Limit of a Reciprocal Function

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Homework Help Overview

The discussion revolves around proving a limit involving a reciprocal function, specifically that if the limit of F(x) approaches infinity as x approaches a, then the limit of 1/F(x) approaches 0. The subject area includes concepts of limits and continuity, particularly in the context of delta-epsilon proofs.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the definitions of limits and how they relate to the behavior of reciprocal functions. There are attempts to apply the definition of limits approaching infinity, with some confusion about the implications for the reciprocal function.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the limit definitions. Some have provided insights into the definitions, while others express confusion about applying these concepts to the specific limit involving 1/F(x).

Contextual Notes

Participants mention constraints related to their current understanding of limits and continuity, specifically referencing delta-epsilon proofs. There is also a recognition of the need for clarity regarding the definitions being used in the context of the problem.

Bigo75
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Homework Statement


Prove: If the Lim as x goes to a of F(x)=infinity, then lim as x goes to a of 1/F(x)=0


Homework Equations



We have only gone over limits and continuity using delta epsilion proofs.
 
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what have you tried? this is straightforward in the sense that it follows from the definitions

show us what you have tried
 
Since the limit is equal to infinity I took an M greater than zero such that X>M implies |F(x)-L| is less than epsilon but I get confused with the one over F(x)=0
 
am I on the right track? I am really confused!
 
Bigo75 said:
Since the limit is equal to infinity I took an M greater than zero such that X>M implies |F(x)-L| is less than epsilon but I get confused with the one over F(x)=0

this is wrong, lim x->a F(x) = inf means for all M > 0 there is a d > 0 s.t. |x-a| < d implies |F(x)| > M. (you can actually drop the absolute value sign here but i'll leave it)
 
ok I understand this definition but how does that help me get lim as x goes to a of 1/f(x)=0? This definition will help me prove another one I was having trouble with. thank you.
 

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