Write Taylor's formula for $f(x)=e^{-x}$ at $x=0,$ with the sbith degree remainde

Select one:

a$.e^{-x}=1-x\frac{x^3}{2}-\frac{x^2}{3}\frac{x^4}{4}-\frac{x^3}{5}\frac{lo{n}^{-6}}{6}{x}^6$

b$.e^{-x}=1-x\frac{x^2}{2}\frac{x^3}{6}\frac{x^4}{24}\frac{x^3}{120}\frac{e^{-3}}{720}{x}^6$

c$.e^{-x}=1x\frac{x^3}{2}\frac{x^3}{3}\frac{x^4}{4}\frac{x^3}{5}\frac{x^{-x}}{6}{x}^6$

d$.e^{-x}=1-x\frac{x^2}{2}-\frac{x^3}{6}\frac{x^4}{4}-\frac{x^3}{100}\frac{x^{-2}}{90}{x}^6$