The problem involves evaluating the 30th derivative of a function at a specific point, using the Taylor polynomial of degree 100 centered at x=3. The polynomial is expressed in terms of powers of (x-3) and factorials, leading to a question about the coefficients related to the derivatives of the function.
Participants are actively questioning the structure of the Taylor polynomial and how to identify the relevant terms for f^{(30)}(3). Some guidance has been provided regarding the general form of the term in the expansion, but there remains uncertainty about how to derive the numerator associated with the 30th derivative.
There is confusion regarding the notation and the relationship between the Taylor series terms and the derivatives of the function. Participants are also navigating the implications of the polynomial's degree and the specific derivatives involved.
See here.yeahyeah<3 said:how do you get the math problem to look like that -.-
That's what it looks like in p(x), but if you didn't know of p(x), what would the term look like?i think the term looks like
(x-3)^30
15!
?
Yes, that kind of thing. So now you know what the general form of the term looks like and what it actually is. I leave the rest to you.yeahyeah<3 said:like f'(30) (x-3)^30 kind of thing?
30!