Good morning,

I am working on Taylor Polynomials this morning, and am not entirely sure I understand what I am supposed to be doing. Would someone mind telling me if the following makes sense?

Compute the Maclaurin Polynomials of degree one, two, and three for $\displaystyle f(x) = e^{-2x}$

As I understand this the fact that this is a Maclaurin Polynomial simply means that the term $\displaystyle (x-a)^n$ becomes simply $\displaystyle x^n $.

I get the following:

$\displaystyle f'(x)=-2e^{-2x}$

$\displaystyle f''(x)=4e^{-2x}$

$\displaystyle f'''(x)=-8e^{-2x}$

$\displaystyle f'(0)=-2$

$\displaystyle f''(0)=4$

$\displaystyle f'''(0)=-8$

$\displaystyle T_1(x)=1-2x$

$\displaystyle T_2(x)=(2x-1)^2$

$\displaystyle T_3(x)=-8x^3+4x^2-2x+1$

Am I way off target here?