Understanding the Limit Notation: Is f(rh,h) the Same as f(r+h)-f(h)?

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Discussion Overview

The discussion revolves around the notation and meaning of the expression f(rh,h) in the context of limits, specifically whether it is equivalent to f(r+h)-f(h). Participants explore the implications of this notation and its application in limit calculations.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether f(rh,h) is the same as f(r+h)-f(h), expressing uncertainty about the notation and its meaning.
  • Another participant confirms that f is a function of two variables, suggesting that the notation implies this relationship.
  • A later reply clarifies that the limit expression involves evaluating f at the point (rh,h) and then dividing by h, but does not resolve the initial question about equivalence with f(r+h)-f(h).

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether f(rh,h) is equivalent to f(r+h)-f(h). The discussion includes both agreement on the function's dimensionality and ongoing uncertainty regarding the specific notation.

Contextual Notes

There is a lack of clarity regarding the assumptions behind the notation and its implications for limit evaluation. The discussion does not resolve the mathematical steps involved in establishing equivalence.

KUphysstudent
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Limh→0+ (f(rh,h))/h
Is the f(rh,h) part the same as f(r+h)-f(h)? I have never seen this before and googling for a long time didn't help, there are no videos with this notation and it's not in my book so, am I just to assume it is? because it doesn't look like it should be the same.

Anyone know what f(rh,h) means? :)
 
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KUphysstudent said:
Limh→0+ (f(rh,h))/h
Is the f(rh,h) part the same as f(r+h)-f(h)? I have never seen this before and googling for a long time didn't help, there are no videos with this notation and it's not in my book so, am I just to assume it is? because it doesn't look like it should be the same.

Anyone know what f(rh,h) means? :)

Is f a function of 2 variables?
 
Math_QED said:
Is f a function of 2 variables?
Yes it is, how did you know? :P
 
KUphysstudent said:
Yes it is, how did you know? :P

The notation suggested it.

The limit in your question is simply

##\lim_{h \to 0+} \frac{f(rh,h)}{h}##

This means that you evaluate ##f## in the point ##(rh,h)## and then take the limit after dividing the result by h.
 
Math_QED said:
The notation suggested it.

The limit in your question is simply

##\lim_{h \to 0+} \frac{f(rh,h)}{h}##

This means that you evaluate ##f## in the point ##(rh,h)## and then take the limit after dividing the result by h.

Oh it was this simple. I was afraid to get guess but thanks really helped me :)
 

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