What is the Definition of Continuity for Functions and How Can It Be Proven?

  • Thread starter curlyc3
  • Start date
  • Tags
    Analysis
In summary, the conversation discussed the definition of continuity for a function at a point, and provided examples to demonstrate continuity and non-continuity.
  • #1
curlyc3
1
0
Hi! I'm struggling with analysis at the moment and here's one question that I'm struggling with! COuld somebody please explain what I need to do, using a delta/epsilon definition
The question is:

Define what it means for a function f to be continuous at a point a.

(a) Prove directly from your definition that f(x) = x^3 is continuous
everywhere.

(b) Give an example of a function that is continuous except at
x = 1, where it is not continuous.

Thanks
 
Physics news on Phys.org
  • #2
u can see the reply of Matt Grime in the post epsilon and delta...
 
  • #3
(b) Give an example of a function that is continuous except at
x = 1, where it is not continuous.

f(x)=0 ,x<1
f(x)=1 ,x>1
 
  • #4
curlyc3 said:
(b) Give an example of a function that is continuous except at
x = 1, where it is not continuous.

Thanks
[tex]f(x)=2.3456712345, x\neq{1}, f(1)=-\frac{\pi^{tan(Sinh(0.5))}}{3.77}[/tex]
 
Last edited:

Related to What is the Definition of Continuity for Functions and How Can It Be Proven?

1. What is the first step in analyzing math problems?

The first step in analyzing math problems is to carefully read and understand the problem. This involves identifying the given information, what needs to be solved for, and any relevant equations or formulas.

2. How can I improve my problem-solving skills in math?

One way to improve problem-solving skills in math is to practice regularly. This can involve solving various types of problems, using different methods and approaches, and seeking help or feedback when needed.

3. What is the importance of breaking down a math problem into smaller steps?

Breaking down a math problem into smaller steps can help make the problem more manageable and easier to solve. It also allows for easier identification of errors and helps to ensure that all necessary information has been considered.

4. How can I check my work for accuracy in math analysis?

One way to check for accuracy in math analysis is to work backwards, plugging the found solution back into the original problem to see if it satisfies all the given conditions. Another way is to use estimation or approximation techniques to see if the solution is reasonable.

5. What should I do if I am still struggling with analyzing math problems?

If you are still struggling with analyzing math problems, seek help from a teacher, tutor, or classmate. They may be able to offer a different perspective or provide additional guidance and resources. Additionally, consider breaking the problem down into smaller steps and practicing with similar problems to build your skills and confidence.

Similar threads

Replies
9
Views
1K
  • Calculus
Replies
25
Views
1K
Replies
9
Views
940
  • Calculus and Beyond Homework Help
Replies
22
Views
444
Replies
3
Views
1K
Replies
36
Views
4K
  • Calculus
Replies
9
Views
2K
Replies
23
Views
3K
Back
Top