Calculus, Delta- Epsilon Proof Of Limits

In summary, the conversation is about proving a statement using the delta epsilon definition. The conclusion is that by choosing a constant C that is not equal to zero, the equation follows and the product of absolute values is equal to the absolute value of the products. The calculations can be found in the attached document.
  • #1
goofyfootsp
12
0

Homework Statement


Is this the right direction to prove

Given that , prove that . Using the delta epsilon definition to prove that means that, for any arbitrary small there exists a where as:




If we choose any constant for (x) called C, as long as C does not equal zero, the equation follows:



whenever , since f(x) as x goes to a is equal to L.

Multiply the by the absolute vale of the constant C, , so you have



Now the product of absolute values is equal to the absolute value of the products so,




The Attempt at a Solution

 

Attachments

  • Limit proof.doc
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  • #2
There appear to be whole sections of your post missing!
 
  • #3
calculations in attachment

I apologize but the attatchment has the work in it.
 

Related to Calculus, Delta- Epsilon Proof Of Limits

1. What is a limit in calculus?

A limit in calculus is the value that a function approaches as the input value gets closer and closer to a specific value. It is denoted by the symbol "lim" and is an important concept in calculus for understanding the behavior of functions.

2. How is a limit calculated?

A limit can be calculated using the concept of delta-epsilon proof. This involves finding a value for delta, which represents the distance between the input value and the specific value, and a value for epsilon, which represents the desired range of output values. By finding a combination of delta and epsilon that satisfies the limit definition, the limit can be calculated.

3. What is the significance of delta-epsilon proof in calculus?

Delta-epsilon proof is significant in calculus because it provides a rigorous and formal way to prove the existence of a limit. It also allows for the calculation of limits for more complex and challenging functions.

4. Can a limit exist even if the function is not defined at that specific point?

Yes, a limit can exist even if the function is not defined at a specific point. This is because a limit is based on the behavior of the function as the input value approaches that point, not necessarily the value at that point itself.

5. How is the concept of delta-epsilon proof applied in real-world situations?

The concept of delta-epsilon proof is applied in real-world situations, particularly in fields such as physics and engineering, to model and analyze the behavior of various systems. It allows for the prediction of values and behaviors based on known data and can be used to optimize and improve systems.

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