What does delta mean in calculus limits?

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In summary, the conversation involves a student struggling with a calculus problem that involves finding the limit of a function. The student is confused about the use of delta x and does not understand its meaning in this context. They mention that their book does not provide an explanation either. Another person suggests replacing delta x with a more friendly variable and working through the problem using algebra. The student then confirms that they have worked out the problem and gotten 2x - 4 + a, but are unsure if it is correct.
  • #1
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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  • #2
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.
 
  • #3
oh so it changes nothing?
 
  • #4
or what am i supposed to do with the delta x value?
 
  • #5
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.
 
  • #6
Trust me. I have read the entire chapter looking for something explaining the delta and there is nothing. Thanks for the tip though.
 
  • #7
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...
 
  • #8
You should have gotten [itex]2x - 4 + a[/itex]. Recheck your algebra.
 

What does delta mean in calculus limits?

Delta, denoted by the Greek letter δ, represents the change in a variable in a given function. In the context of calculus limits, delta is used to refer to the change in the input variable as it approaches a specific value.

How is delta used in calculus limits?

In calculus limits, delta is typically used as part of the definition of a limit. It signifies the distance between the input variable and the specific value it is approaching. This distance is then used to determine the behavior of the function as the input variable gets closer and closer to the specific value.

What is the significance of delta in calculus limits?

Delta is a crucial concept in calculus limits as it helps us understand the behavior of a function at specific points. It allows us to analyze how the function changes as the input variable approaches a certain value, which is essential in finding the limit of a function.

Can delta be used to find the precise value of a limit?

No, delta alone cannot be used to find the precise value of a limit. It is only used to describe the behavior of a function as the input variable approaches a specific value. To find the precise value of a limit, additional techniques such as substitution or evaluating the function at the specific value are necessary.

How can one determine the value of delta in calculus limits?

The value of delta is not predetermined and can vary depending on the function and the specific value it is approaching. It can be calculated by considering the behavior of the function and the desired level of accuracy. Generally, a smaller delta value will result in a more precise limit value, but it can also make calculations more complex.

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