# Taylor Polynomial & Remainder

• May 7th 2008, 10:57 AM
kithy
Taylor Polynomial & Remainder
given f(x) = x/(1-x)

a) determine the Taylor polynomial of order 3 to f expanded about x=0

b) write an equation for the remainder term of order 3, R3(x), in the taylor series for f

I don't know how to solve this problem.

any help is greately appreciated

thanks
k
• May 7th 2008, 12:43 PM
o_O
$T_{3}(x) = f(0) + f'(0)x +\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}$

So all you really need is to find f'(0), f''(0), and f'''(0).

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$R_{3}(x) = \underbrace{\frac{f^{(n+1)}(c)}{(n+1)!}x^{n+1}}_{n =3} = \frac{f^{(4)}(c)}{4!}x^{4} \quad c \in (x_{0} = 0, x)$

Find the 4th derivative of f(x) and you should be set.