Remainder for Maclaurin Series

[SeannyBoi71]

Homework Statement

Find the Maclaurin series of $$f(x) = x^2cos(x)$$

Homework Equations

I got the answer to be (sum from n=1 to infinity) $$\frac{(-1)(^n+1)x(^2n)}{(2n-2)!}$$ and the formula for the remainder is $$R_n(x) = \frac{f(^n+1)(c)}{(n+1)!}x(^n+1)$$

(I have no idea how to make those exponents work, So I hope you know what the formula says .)

The Attempt at a Solution

I am pretty sure the answer (not including the remainder) is correct, I just have no idea how to find the remainder using that formula. Don't even know how to apply it.

EDIT: Is it even necessary to find the remainder? Whenever I watch a tutorial on Maclaurin series they never find the remainder... so should I just assume that the Maclaurin series is a good representation of f(x) without calculating the remainder?

 

[Ray Vickson]

Homework Statement

Find the Maclaurin series of $$f(x) = x^2cos(x)$$

Homework Equations

I got the answer to be (sum from n=1 to infinity) $$\frac{(-1)(^n+1)x(^2n)}{(2n-2)!}$$ and the formula for the remainder is $$R_n(x) = \frac{f(^n+1)(c)}{(n+1)!}x(^n+1)$$

(I have no idea how to make those exponents work, So I hope you know what the formula says .)

The Attempt at a Solution

I am pretty sure the answer (not including the remainder) is correct, I just have no idea how to find the remainder using that formula. Don't even know how to apply it.

EDIT: Is it even necessary to find the remainder? Whenever I watch a tutorial on Maclaurin series they never find the remainder... so should I just assume that the Maclaurin series is a good representation of f(x) without calculating the remainder?

Of course it is sometimes important to know the form of the remainder (for example, when analyzing the accuracy of some numerical integration methods, etc). Never assume that the Maclaurin series is _necessarily_ a good representation of f(x); sometimes it is, and sometimes not; it depends on the range of x and the behavior of f, etc.

RGV

 

[SeannyBoi71]

Of course it is sometimes important to know the form of the remainder (for example, when analyzing the accuracy of some numerical integration methods, etc). Never assume that the Maclaurin series is _necessarily_ a good representation of f(x); sometimes it is, and sometimes not; it depends on the range of x and the behavior of f, etc.

RGV

I just noticed that another question on the assignment asks specifically "Find the 3rd degree Taylor polynomals and the remainders at a = 1 for the following functions." The first question doesn't say that... So I'm thinking he does not want us to bother finding it...