Taylor approximation Any function $f(x)$ can be written as an infinite series in the vicinity of $x=0$ using a Taylor expansion. Because $x$ is small, every term is smaller than all the terms before it:

$f(x)$~~$f(0)+x(\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}){|}_x||=0+\frac{1}{2!}{x}^2(\frac{de{l}^{2}f}{del{x}^2}){|}_x||=0+$dots

write the first three terms of a Taylor expansion for the following functions

$($a$)f(x)=$exp$(-ax)$

$($b$)f(x)=(1+bx{)}^{-2}$