Help with delta-epsilon notation

  • Thread starter PvtBillPilgrim3
  • Start date
  • Tags
    Notation
In summary, for a given epsilon e > 0, a delta d can be found such that for all x, abs(x) < d, the absolute value of [(x^2 - x + 1)/(x+1)] - 1 is less than e. The equation provided in the attempt at a solution is incorrect, but once corrected, the same delta can be used to find the desired result.
  • #1
PvtBillPilgrim3
5
0

Homework Statement


For a given epsilon e > 0, I need to find a delta d such that for all x, abs(x) < d:

abs([(x^2 - x + 1)/(x+1)] - 1) < e


Homework Equations





The Attempt at a Solution


I get the absolute value of:
x^2 - 2x
--------, which is less than or equal to the absolute value of
x + 1

x^2 - 2x
--------, which equals the absolute value
x

x-2, which is less than or equal to

abs(x) + 2.

How do I then find the delta for this and is this right?
 
Physics news on Phys.org
  • #2
I don't think your equation is correct. Once it's corrected, pretend the singularity doesn't exist, and the same delta should work.
 

1. What is delta-epsilon notation?

Delta-epsilon notation is a mathematical notation used to define the limit of a function. It is commonly used in calculus to formally prove the limit of a function as it approaches a specific value.

2. Why is delta-epsilon notation important?

Delta-epsilon notation is important because it provides a rigorous and precise way to define and prove the limit of a function. It allows for a more accurate understanding of the behavior of a function near a particular point.

3. How is delta-epsilon notation used?

Delta-epsilon notation is used by first defining the limit of a function using the symbols delta (Δ) and epsilon (ε). Then, the notation is used to prove the limit of the function by showing that for any given value of epsilon, there exists a corresponding value of delta that satisfies the definition.

4. What are some common mistakes when working with delta-epsilon notation?

Some common mistakes when working with delta-epsilon notation include not properly understanding the definition of the limit, using the wrong symbols or notations, and not following the logical steps in the proof.

5. Are there any alternative notations for defining the limit of a function?

Yes, there are alternative notations for defining the limit of a function, such as the arrow notation (lim x→a f(x)) and the functional notation (f(a)). However, delta-epsilon notation is the most commonly used notation for formal proofs of limits in calculus.

Similar threads

  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
1K
  • Calculus and Beyond Homework Help
Replies
13
Views
2K
  • Calculus and Beyond Homework Help
Replies
7
Views
135
  • Calculus and Beyond Homework Help
Replies
9
Views
462
  • Calculus and Beyond Homework Help
Replies
16
Views
1K
  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
84
  • Calculus and Beyond Homework Help
Replies
0
Views
69
  • Calculus and Beyond Homework Help
Replies
2
Views
669
Back
Top