Why is the Precise Definition of a Limit So Confusing?

In summary, the speaker expresses their struggle with understanding the precise definition of a limit in calculus, with a strong emotional reaction. They wonder if anyone else feels the same way and apologize for posting in the wrong place. The listener offers reassurance and suggests using a visual aid to better understand the concept.
  • #1
efekwulsemmay
54
0
Ok, with my second time around taking calculus 1 I am finally beginning to understand the whole concept of the Precise definition of a limit. However, I hate them. Never before in my life have I had the feeling or a need to drink, smoke, drive at 100mph and kill someone all at the same time! (Disclosure: I am not planning on killing anyone. Calm down. I just feel like it...) With all the epsilons and their corresponding deltas and the absolute value of the function values. Just GAAAH! And GRRRRRRRR! And all that jazz.
Does anyone else feel this way? Am I alone on this one or what?
(/rant)

Thank you for your time.

(p.s. Wasn't sure where to put this so I put it here. If here was the wrong place I apologize. Just point out to me were I should have posted this and I will do so next time.)
 
Physics news on Phys.org
  • #2
You are defiantly alone!jkz

Actually, it takes a while for the definition to sink in. Even capable math majors have a tough time with it.

Draw a picture, it will help.
 

What is a precise definition of a limit?

A limit is a fundamental concept in calculus that describes the behavior of a function as the input value approaches a certain point. It is defined as the value that the function approaches as the input value gets closer and closer to the specified point.

How is a limit expressed mathematically?

A limit is expressed mathematically using the notation "lim f(x)" where f(x) is the function and the limit is taken as x approaches a specific value or approaches infinity. For example, "lim x→a f(x)" represents the limit of the function f(x) as x approaches the value a.

What is the epsilon-delta definition of a limit?

The epsilon-delta definition of a limit is a way to formally define a limit using the concepts of distance and precision. It states that for any given distance (epsilon), there exists a corresponding distance (delta) such that if the input value is within that distance from the specified point, then the output value of the function will be within the given distance from the limit.

What is the importance of a precise definition of a limit?

The precise definition of a limit is crucial in calculus, as it allows us to rigorously prove the behavior of functions as they approach specific values. It also forms the basis for many important theorems and concepts in calculus, such as continuity and differentiability.

How do you evaluate a limit using the precise definition?

To evaluate a limit using the precise definition, we must first determine the values of epsilon and delta that satisfy the definition. Then, we can use algebraic manipulation and the properties of limits to simplify the expression and find the limit. Alternatively, we can use graphical or numerical methods to approximate the limit.

Similar threads

Replies
18
Views
1K
  • Calculus
Replies
4
Views
1K
Replies
13
Views
2K
Replies
4
Views
2K
Replies
2
Views
968
Replies
8
Views
2K
Replies
8
Views
3K
Replies
4
Views
978
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
227
Back
Top