A community for students.
Here's the question you clicked on:
 0 viewing
akl3644
 3 years ago
taylor expansion question: what part of the expansion of a function of f(x) in powers of x best reflects the behavior of the function for x's close to 0?
akl3644
 3 years ago
taylor expansion question: what part of the expansion of a function of f(x) in powers of x best reflects the behavior of the function for x's close to 0?

This Question is Closed

akl3644
 3 years ago
Best ResponseYou've already chosen the best response.0@KingGeorge can you help me on this question?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Well, if we divide it up into parts where a "part" is the first n terms, I have an idea. However, I would like to see what you think before I start an explanation.

akl3644
 3 years ago
Best ResponseYou've already chosen the best response.0i am really confuse abt this question. i don't know what is ask for

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Well, it's talking about the powers of x. From that, I would make a guess that they want you to say that it's the all the terms up to the \(x^1\)th term. However, there's no real way to say for sure since this isn't necessarily a McLaurin Series. Thus, it's not necessarily centered at 0, so it really depends on the function.

akl3644
 3 years ago
Best ResponseYou've already chosen the best response.0what if the curve is centered at 0?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1However, if we assume it is centered at 0, then let's throw away all the terms except the first two terms. So we have a function that looks like \(T_1(x)=ax+b\). It is precisely correct at \(x=0\) since it's centered at 0, and for very close points, it has nearly the same slope. So for points very close to \(x=0\), this is a good approximation.

akl3644
 3 years ago
Best ResponseYou've already chosen the best response.0is could apply every function if the function is centered at 0?

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1If it's centered at 0, I would say the first two terms. If it's not centered at 0, you really can't say anything. However, the best approximation, is the whole Taylor series.

KingGeorge
 3 years ago
Best ResponseYou've already chosen the best response.1Of course, if you use the whole thing, it shouldn't be an approximation anymore. It would be exactly the same.

akl3644
 3 years ago
Best ResponseYou've already chosen the best response.0ok! thank you very much!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.