Converging to Delta(y-b): Solving the Limit of f_x((y-b)/a) as a Approaches 0

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Discussion Overview

The discussion revolves around the limit of a function as a parameter approaches zero, specifically examining the expression lim 1/|a| f_x((y-b)/a) and its convergence to delta(y-b). The scope includes theoretical aspects of limits and possibly the properties of the Dirac delta function.

Discussion Character

  • Exploratory, Debate/contested

Main Points Raised

  • One participant requests clarification on the definition of "delta(y-b)," suggesting it may refer to the Dirac delta function.
  • Another participant seeks to understand what f_x represents in this context.
  • There is a repeated assertion of the limit converging to delta(y-b), but the problem definition is noted as unclear by some participants.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the definitions of key terms and the clarity of the problem, indicating that multiple competing views remain without consensus on the definitions involved.

Contextual Notes

The discussion highlights limitations in the problem definition and the need for clearer definitions of "delta(y-b)" and "f_x." There are unresolved questions about the assumptions underlying the limit being discussed.

luppin
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Show the following limit will converge to delta(y-b),

lim 1/|a| f_x((y-b)/a)=delta(y-b)
a-->0
 
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How are you defining "delta(y- b)"?
 
And what is [math]f_x[/math]?

-Dan
 
luppin said:
Show the following limit will converge to delta(y-b),

lim 1/|a| f_x((y-b)/a)=delta(y-b)
a-->0

Problem definition is not clear.
 

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