What does delta mean in calculus limits?

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Discussion Overview

The discussion revolves around the meaning of delta (∆) in the context of calculus limits, particularly in the expression for the limit of a function as the change in x approaches zero. Participants explore the implications of this notation and how to approach solving a specific limit problem.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the meaning of delta in the limit expression, noting that their textbook does not provide an explanation.
  • Another participant explains that delta x approaching zero indicates that the change in x is becoming very small, almost zero.
  • A participant questions whether delta x changes anything in the context of the problem.
  • There is a suggestion to replace delta x with a different variable (a) to simplify the algebra and understand the limit as a approaches zero.
  • A participant reports working through the problem and arriving at an expression of 2x + a, expressing uncertainty about its correctness.
  • Another participant challenges this result, suggesting that the correct expression should be 2x - 4 + a and advises rechecking the algebra.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to the problem or the interpretation of delta. There are competing views on how to handle the delta notation and uncertainty regarding the correctness of the algebraic manipulation.

Contextual Notes

Some participants express limitations in their understanding due to a lack of explanation in their textbook, and there are unresolved questions about the algebraic steps taken in the problem-solving process.

kendal12
I just started calculus and we are doing limits. I was doing fine on my hmwrk until i came to this problem:

Find lim f(x+∆x) – f(x)/ ∆x
∆x→0

f(x)= x^2 – 4x

I have no idea what the delta means... I know in chem it means "a change in", but I don't know what to do with it here. My book doesn't explain it either. Please help! Thanks
 
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delta x ->0
means as x approaches zero

or in other words the change in the value of x is getting so small that it is almost zero.
 
oh so it changes nothing?
 
or what am i supposed to do with the delta x value?
 
kendal,

My book doesn't explain it either.

I seriously doubt that. For purposes of solving your problem and to get you accustomed to the concept why don't you just replace the [itex]\Delta x[/itex] with something more friendly looking like a? Then you can carry out your algebra and examine what happens when a is made arbitrarily small.
 
Trust me. I have read the entire chapter looking for something explaining the delta and there is nothing. Thanks for the tip though.
 
ok, so I worked out the problem and got 2x+a... is this correct? For some reason I don't think it is, but I thought I worked it out right...
 
You should have gotten [itex]2x - 4 + a[/itex]. Recheck your algebra.
 

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