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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?
 one year ago
 one year 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?
 one year ago
 one year ago

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akl3644Best ResponseYou've already chosen the best response.0
@KingGeorge can you help me on this question?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Well, 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.
 one year ago

akl3644Best ResponseYou've already chosen the best response.0
i am really confuse abt this question. i don't know what is ask for
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
Well, 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.
 one year ago

akl3644Best ResponseYou've already chosen the best response.0
what if the curve is centered at 0?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
However, 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.
 one year ago

akl3644Best ResponseYou've already chosen the best response.0
is could apply every function if the function is centered at 0?
 one year ago

KingGeorgeBest ResponseYou've already chosen the best response.1
If 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.
 one year ago

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

akl3644Best ResponseYou've already chosen the best response.0
ok! thank you very much!!
 one year ago
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