Tips for doing proofs in calculus

[KataKoniK]

Hi,

I have a major test next week and some questions will be on epsilon and delta proofs. From the homework I have done, these epsilon and delta proofs can be applied anywhere and in any scenario. Therefore, I was wondering do you guys have any tips on handling and solving these questions?

Thanks in advance.

 

[Galileo]

Yeah. Practice.

Practice a lot...

 

[M98Ranger]

Hi there,

Here are some tips for doing proofs in calculus, specifically epsilon and delta proofs:

1. Understand the definitions: The key to mastering epsilon and delta proofs is to have a clear understanding of the definitions of limits, continuity, and differentiability. Make sure you know these definitions inside out before attempting any proofs.

2. Start with the given: Before attempting to prove anything, start by writing down the given information and what you need to prove. This will help you stay organized and focused throughout the proof.

3. Use the definition of a limit: Epsilon and delta proofs are all about proving that a limit exists, so make sure to use the definition of a limit in your proof. This means showing that for any epsilon (small number), there exists a delta (another small number) such that the distance between the function and the limit is less than epsilon whenever the distance between the input and the limit is less than delta.

4. Work backwards: When approaching a proof, it can be helpful to work backwards from what you need to prove to the given information. This can help you see the steps you need to take and make the proof more manageable.

5. Use algebraic manipulation: Epsilon and delta proofs often involve manipulating equations to get them into a form that is easier to work with. Make sure to use algebraic manipulation to your advantage in these proofs.

6. Practice, practice, practice: Like with any other skill, practice makes perfect when it comes to doing proofs in calculus. Make sure to do lots of practice problems, and don't be afraid to ask for help if you get stuck.

Good luck on your test!