Understanding Taylor Polynomials for Calc-2

In summary, the conversation revolved around the topic of understanding and visualizing Taylor approximation in calculus. The individual was having difficulty grasping the concept, but had no trouble completing homework on the topic. They requested an explanation on how to think about approximations using Taylor Polynomials. The other person recommended referring to a blog post they had written on the subject and offered to answer any questions. The individual expressed gratitude and mentioned needing time to fully understand the information.
  • #1
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Hi,
I'm doing calc-2, and I have hard time understanding and visualizing the idea of Taylor approximation in my head. By the same time I have no problems solving homework on this topic.

Can someone please explain how I should visualize and think about approximations using Taylor Polynomials to really understand this...
 
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  • #2
I'm going to take the liberty of referring you to https://www.physicsforums.com/blog.php?b=1758 , which I wrote some time ago.

I hope it gets you started, if you have any questions, please feel free to ask.
 
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  • #3
Oh..., great post!
Now I need some time to digest this in my mind...=)
I'm already have a question but need time to formulate it clearly...
Again, thank you very much!
 

1. What is the purpose of Taylor polynomials in Calc-2?

The purpose of Taylor polynomials is to approximate a function at a specific point using a polynomial of a certain degree. This allows us to simplify complicated functions and make them easier to work with in calculus.

2. How are Taylor polynomials different from regular polynomials?

Taylor polynomials are different from regular polynomials because they are centered at a specific point and are designed to approximate a function at that point. Regular polynomials do not have a specific point of reference and are used to represent a function across its entire domain.

3. What is the process for finding a Taylor polynomial?

The process for finding a Taylor polynomial involves taking derivatives of the function at the specific point and plugging in the values into the polynomial formula. The degree of the polynomial will depend on how many derivatives are taken.

4. How do Taylor polynomials help in understanding the behavior of a function?

Taylor polynomials help in understanding the behavior of a function by providing a close approximation at a specific point. This allows us to analyze the behavior of the function near that point and make predictions about its behavior at other points.

5. Can Taylor polynomials be used to find the exact value of a function?

No, Taylor polynomials can only approximate a function at a specific point. The more terms that are included in the polynomial, the closer the approximation will be to the actual value of the function at that point, but it will never be exact.

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