Proving the Limit of Zero Using Epsilon-Delta Method

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In summary, the conversation discusses the writing of an epsilon-delta proof for the limit of 0 as x approaches 2. The person is struggling with using epsilon and delta to prove the limit, but is given hints and advice from others. They eventually thank everyone for their help.
  • #1
savtaylor2010
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Epsilon-Delta proof of zero??

Homework Statement



Write an epsilon delta proof for the limx[itex]\rightarrow[/itex]2 0 = 0.


The Attempt at a Solution



This is for my discrete math class. I know how to do limit proofs with a variable, like x or x2, but it seems that this is obvious that the limit approaching zero is zero. It is so easy, that it is hard for me to use epsilon and delta to prove. I don't know really where to start for this one. I would appreciate some hints and help!
 
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  • #2


savtaylor2010 said:

Homework Statement



Write an epsilon delta proof for the limx[itex]\rightarrow[/itex]2 0 = 0.


The Attempt at a Solution



This is for my discrete math class. I know how to do limit proofs with a variable, like x or x2, but it seems that this is obvious that the limit approaching zero is zero. It is so easy, that it is hard for me to use epsilon and delta to prove. I don't know really where to start for this one. I would appreciate some hints and help!

It might help to call f(x) = 0. Write down the definition as you would with f(x) and L and replace f(x) and L by 0.
 
  • #3


Start by choosing an epsilon maybe let epsilon equal something really close to 0 like 0.2

and assume that x-2< alpha . so that you can so that 0<ε .
 
  • #4


savtaylor2010 said:

Homework Statement



Write an epsilon delta proof for the limx[itex]\rightarrow[/itex]2 0 = 0.


The Attempt at a Solution



This is for my discrete math class. I know how to do limit proofs with a variable, like x or x2, but it seems that this is obvious that the limit approaching zero is zero. It is so easy, that it is hard for me to use epsilon and delta to prove. I don't know really where to start for this one. I would appreciate some hints and help!

hint: the proof is eactly the same if you replace 0 by c, where c is any constant. that is, if you replace the function f(x) = 0 with g(x) = c, the same argument works for both (the "delta" is really easy to find, for any "epsilon").
 
  • #5


Thank you guys for all of your help! I know I am really late responding back, but all of the feedback really helped!
 

FAQ: Proving the Limit of Zero Using Epsilon-Delta Method

What is an Epsilon-Delta proof of zero?

An Epsilon-Delta proof of zero is a mathematical method used to prove that the limit of a function is equal to zero. It involves showing that for any small value of epsilon (ε), there exists a corresponding value of delta (δ) such that when the input is within a certain distance (δ) from zero, the output will be within a certain distance (ε) from zero.

Why is an Epsilon-Delta proof used to prove zero?

An Epsilon-Delta proof is used to prove zero because it provides a rigorous and precise method for showing that a limit is equal to zero. This proof is commonly used in calculus and analysis to prove the convergence of a sequence or the continuity of a function at a certain point.

How is an Epsilon-Delta proof of zero written?

An Epsilon-Delta proof of zero is typically written in the form of a logical argument. It begins with a statement of the limit definition and then proceeds to show how the values of epsilon and delta are chosen to satisfy the definition. This is followed by a series of mathematical steps to prove that the limit is equal to zero.

What are the key elements of an Epsilon-Delta proof of zero?

The key elements of an Epsilon-Delta proof of zero are the use of the limit definition, the choice of epsilon and delta values, and the logical steps used to show that the limit is equal to zero. It is also important to clearly state any assumptions made and to carefully justify each step in the proof.

How can I improve my understanding of Epsilon-Delta proofs of zero?

To improve your understanding of Epsilon-Delta proofs of zero, it is recommended to practice solving various examples and exercises. You can also seek help from a tutor or attend study groups to discuss and clarify any questions you may have. Additionally, reading and understanding different proofs and their techniques can also enhance your understanding of this topic.

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