If numerator is zero, then limit is infinite?

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Homework Help Overview

The discussion revolves around the concept of limits in calculus, specifically focusing on the behavior of rational expressions where the numerator is zero. Participants explore the implications of limits as variables approach specific values or infinity.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Some participants present examples of limits involving zero in the numerator and discuss the outcomes, while others raise questions about scenarios where both the numerator and denominator approach zero, suggesting that the limit could vary widely in such cases.

Discussion Status

The discussion is ongoing, with participants sharing their understanding of limits involving zero and questioning the assumptions related to different cases. There is acknowledgment of the complexity introduced when both the numerator and denominator approach zero.

Contextual Notes

Participants are navigating the nuances of limit behavior under specific conditions, particularly focusing on the implications of having zero in the numerator and the potential for indeterminate forms when both the numerator and denominator approach zero.

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please someone aware me
 
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lim x-> a (0/x) = 0

and

lim x-> +/- infinity (0/x) = 0

Since 0/x = 0 for all nonzero x
 
thanks
 
JG89 said:
lim x-> a (0/x) = 0

and

lim x-> +/- infinity (0/x) = 0

Since 0/x = 0 for all nonzero x

But, if both the numerator and denominator are approaching zero, then all bets are off. The limit of this rational expression could be any real number or infinite.
 

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